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1.
Field, Scott Edward.
Applications of Discontinuous Galerkin Methods to
Computational General Relativity.
Degree: PhD, Physics, 2011, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:11327/ 
► We discuss a discontinuous Galerkin (dG) method and its application to common partial differential equations which arise in the context of general relativity. First we…
(more)
▼ We discuss a discontinuous Galerkin (dG) method and
its application to common partial differential equations which
arise in the context of general
relativity. First we consider
extreme mass ratio binary (EMRB) systems. When modeling EMRBs as
perturbations of a Schwarzschild black hole, the metric
perturbations are described by the distributionally forced
Regge-Wheeler-Zerilli (RWZ) equation. Despite the presence of jump
discontinuities in the solution, our dG method achieves pointwise
spectral accuracy. Particular attention is given to the common
choice of trivialinitial data, and we show such unphysical
specification may lead to spurious solutionswhich contaminate the
physical solution indefinitely. Unintended consequences of
thepersistent junk solution are considered as well as a simple
prescription for removing it. Using our code we compute metric
perturbations, gravitational waveforms, and self-force measurements
from both circular and eccentric orbits.Next, we present a dG
method for evolving the spherically reduced Generalized
Baumgarte-Shapiro-Shibata-Nakamura (GBSSN) system expressed in
terms of second-order spatial operators. Our multi-domain method
achieves global spectralaccuracy and long-time stability on short
computational domains. We discuss in detail both our scheme for the
GBSSN system and its implementation. A theoretical and
computational verification of the proposed scheme is given.We
conclude with a preliminary look at reduced basis (RB) methods for
parameterized binary systems. Our algorithm aims to construct a
compact RB space from which a particular solution can be quickly
and accurately recovered. We apply the algorithm to compress the
space of analytic chirp gravitational waveforms. Next, the RWZ
equation is revisited, and we consider extensions of the algorithm
to a dG solver along with
numerical evidence that a RB space exists
for EMRB waveforms.
Advisors/Committee Members: Hesthaven, Jan (Director), Guralnik, Gerald (Reader), Dell'Antonio, Ian (Reader).
Subjects/Keywords: Numerical Relativity
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APA (6th Edition):
Field, S. E. (2011). Applications of Discontinuous Galerkin Methods to
Computational General Relativity. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11327/
Chicago Manual of Style (16th Edition):
Field, Scott Edward. “Applications of Discontinuous Galerkin Methods to
Computational General Relativity.” 2011. Doctoral Dissertation, Brown University. Accessed March 01, 2021.
https://repository.library.brown.edu/studio/item/bdr:11327/.
MLA Handbook (7th Edition):
Field, Scott Edward. “Applications of Discontinuous Galerkin Methods to
Computational General Relativity.” 2011. Web. 01 Mar 2021.
Vancouver:
Field SE. Applications of Discontinuous Galerkin Methods to
Computational General Relativity. [Internet] [Doctoral dissertation]. Brown University; 2011. [cited 2021 Mar 01].
Available from: https://repository.library.brown.edu/studio/item/bdr:11327/.
Council of Science Editors:
Field SE. Applications of Discontinuous Galerkin Methods to
Computational General Relativity. [Doctoral Dissertation]. Brown University; 2011. Available from: https://repository.library.brown.edu/studio/item/bdr:11327/
Princeton University
2.
Ripley, Justin Lloyd.
General relativity and its classical modification in gravitational collapse
.
Degree: PhD, 2020, Princeton University
URL: http://arks.princeton.edu/ark:/88435/dsp01v692t926f
► In this thesis, we describe numerical spherical collapse solutions to a ``modified gravity'' theory, Einstein dilaton Gauss-Bonnet (EdGB) gravity. Of the class of all known…
(more)
▼ In this thesis, we describe
numerical spherical collapse solutions to a ``modified gravity'' theory, Einstein dilaton Gauss-Bonnet (EdGB) gravity. Of the class of all known modified gravity theories, EdGB gravity has attracted recent attention due to speculations that the theory may have a classically well-posed initial value formulation and yet also exhibit stable scalarized black hole solutions (what makes this surprising is the plethora of black hole ``no hair theorems'', the assumptions behind which EdGB gravity manages to avoid). If EdGB gravity indeed possess these properties, it would be an ideal theory to perform model-selection tests against general
relativity (GR) in binary black hole merger using gravitational waves. Furthermore, the theory is an important member of the so-called ``Horndeski theories'', which have been invoked to construct, e.g. nonsingular black hole and cosmological solutions, and to address the classical flatness and horizon problems of the early universe.
In constructing
numerical solutions to EdGB gravity (without any approximations beyond the restriction to spherically symmetric configurations), we are able to carefully examine various claims made in the literature about EdGB gravity, perhaps most importantly whether or not the theory admits a classically well-posed initial value problem. One conclusion of these studies has been, at least in spherical collapse, EdGB gravity can \emph{dynamically} lose hyperbolicity, which shows EDGB gravity is fundamentally of ``mixed type''. Mixed type problems appear in earlier problems in mathematical physics, perhaps most notably in the problem of steady state, inviscid, compressible fluid flow. The loss of hyperbolicity and subsequent formation of ``elliptic regions'' outside of any sort of horizon implies that the theory violates cosmic censorship, broadly defined. Arguably it is clear that this result is gauge invariant, although we do not formulate a rigorous proof that this is so. In addition to discussing the hyperbolicity of EdGB gravity, we discuss several other interesting features to the
numerical solutions, including the formation of scalarized black hole solutions in the theory, at least for certain parameter ranges for the theory and certain open sets of initial data.
Advisors/Committee Members: Pretorius, Frans (advisor).
Subjects/Keywords: General Relativity;
Modified Gravity;
Numerical Relativity
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APA (6th Edition):
Ripley, J. L. (2020). General relativity and its classical modification in gravitational collapse
. (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01v692t926f
Chicago Manual of Style (16th Edition):
Ripley, Justin Lloyd. “General relativity and its classical modification in gravitational collapse
.” 2020. Doctoral Dissertation, Princeton University. Accessed March 01, 2021.
http://arks.princeton.edu/ark:/88435/dsp01v692t926f.
MLA Handbook (7th Edition):
Ripley, Justin Lloyd. “General relativity and its classical modification in gravitational collapse
.” 2020. Web. 01 Mar 2021.
Vancouver:
Ripley JL. General relativity and its classical modification in gravitational collapse
. [Internet] [Doctoral dissertation]. Princeton University; 2020. [cited 2021 Mar 01].
Available from: http://arks.princeton.edu/ark:/88435/dsp01v692t926f.
Council of Science Editors:
Ripley JL. General relativity and its classical modification in gravitational collapse
. [Doctoral Dissertation]. Princeton University; 2020. Available from: http://arks.princeton.edu/ark:/88435/dsp01v692t926f
Rochester Institute of Technology
3.
Rosato, Nicole.
Visualization and Analysis of a Numerical Simulation of GW150914.
Degree: MS, School of Mathematical Sciences (COS), 2017, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/9609
► We present a visualization and analysis of a supercomputer simulation displaying the apparent horizons' curvature and radiation emitted from a binary black hole system…
(more)
▼ We present a visualization and analysis of a supercomputer simulation displaying the apparent horizons' curvature and radiation emitted from a binary black hole system modeling the LIGO observed signal GW150914. The simulation follows the system from seven orbits prior to merger down to the resultant final Kerr black hole. Apparent horizons are calculated during the simulation with mean curvature data displayed on them. Radiation data was visualized via the real part of the Ψ
4 component of the Weyl scalars, which were determined using a
numerical quasi-Kinnersley method. We also present a comparative study of the differences in using the quasi-Kinnersley and PsiKadelia tetrads to construct Ψ
4 and the benefits, particularly in the strong field region of a binary black hole system, of using a tetrad in a transverse (Ψ
1=Ψ
3=0) frame. The second part of our studies focus on the relationship between the mean curvature displayed on the apparent horizons and the trajectories of the black holes. We notice that prior to merger, for each black hole, the directionality of the mean curvature tracks that of the trajectory with either a positive or negative phase shift between the two curves. Finally, we provide a brief analysis suggesting that the phase shift and the frame dragging effects are likely related.
Advisors/Committee Members: Carlos Lousto.
Subjects/Keywords: Applied mathematics; Math; Numerical relativity
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APA ·
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APA (6th Edition):
Rosato, N. (2017). Visualization and Analysis of a Numerical Simulation of GW150914. (Masters Thesis). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/9609
Chicago Manual of Style (16th Edition):
Rosato, Nicole. “Visualization and Analysis of a Numerical Simulation of GW150914.” 2017. Masters Thesis, Rochester Institute of Technology. Accessed March 01, 2021.
https://scholarworks.rit.edu/theses/9609.
MLA Handbook (7th Edition):
Rosato, Nicole. “Visualization and Analysis of a Numerical Simulation of GW150914.” 2017. Web. 01 Mar 2021.
Vancouver:
Rosato N. Visualization and Analysis of a Numerical Simulation of GW150914. [Internet] [Masters thesis]. Rochester Institute of Technology; 2017. [cited 2021 Mar 01].
Available from: https://scholarworks.rit.edu/theses/9609.
Council of Science Editors:
Rosato N. Visualization and Analysis of a Numerical Simulation of GW150914. [Masters Thesis]. Rochester Institute of Technology; 2017. Available from: https://scholarworks.rit.edu/theses/9609
Louisiana State University
4.
Calabrese, Gioel.
Constraint preserving boundary conditions for the linearized Einstein equations.
Degree: PhD, Physical Sciences and Mathematics, 2003, Louisiana State University
URL: etd-1105103-100340
;
https://digitalcommons.lsu.edu/gradschool_dissertations/346
► The successful construction of long time convergent finite difference schemes approximating highly gravitating systems in general relativity remains an elusive task. The presence of constraints…
(more)
▼ The successful construction of long time convergent finite difference schemes approximating highly gravitating systems in general relativity remains an elusive task. The presence of constraints and the introduction of artificial time-like boundaries contribute significantly to the difficulty of this problem. Whereas in the absence of boundaries the Bianchi identities ensure that the constraints vanish during evolution provided that they are satisfied initially, this is no longer true when time-like boundaries are introduced. In this work we consider the linearization around the Minkowski space-time in Cartesian coordinates of the generalized Einstein-Christoffel system and analyze different kinds of boundary conditions that are designed to ensure that the constraints vanish throughout the computational domain: the Neumann, Dirichlet, and Sommerfeld cases. In addition to the situation in which the boundary is aligned with a coordinate surface, we examine the presence of corners in the computational domain. We find that, at a corner, there are compatibility conditions which the boundary data and its derivatives must satisfy and that, in general, achieving consistency of a finite difference scheme can be troublesome. We present several numerical experiments aimed at establishing or confirming the well-posedness or ill-posedness of a problem and the consistency of the numerical boundary conditions at the corners. In the case of a smooth boundary we are able to find stable discretizations for all three cases. However, when a corner is present no stable discretization was found for the Sommerfeld case. Finally, we propose an alternative implementation of the Sommerfeld boundary conditions that would preserve the constraints, offer a good approximation for absorbing boundary conditions, and eliminate the problem of the corners.
Subjects/Keywords: numerical relativity
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APA ·
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APA (6th Edition):
Calabrese, G. (2003). Constraint preserving boundary conditions for the linearized Einstein equations. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-1105103-100340 ; https://digitalcommons.lsu.edu/gradschool_dissertations/346
Chicago Manual of Style (16th Edition):
Calabrese, Gioel. “Constraint preserving boundary conditions for the linearized Einstein equations.” 2003. Doctoral Dissertation, Louisiana State University. Accessed March 01, 2021.
etd-1105103-100340 ; https://digitalcommons.lsu.edu/gradschool_dissertations/346.
MLA Handbook (7th Edition):
Calabrese, Gioel. “Constraint preserving boundary conditions for the linearized Einstein equations.” 2003. Web. 01 Mar 2021.
Vancouver:
Calabrese G. Constraint preserving boundary conditions for the linearized Einstein equations. [Internet] [Doctoral dissertation]. Louisiana State University; 2003. [cited 2021 Mar 01].
Available from: etd-1105103-100340 ; https://digitalcommons.lsu.edu/gradschool_dissertations/346.
Council of Science Editors:
Calabrese G. Constraint preserving boundary conditions for the linearized Einstein equations. [Doctoral Dissertation]. Louisiana State University; 2003. Available from: etd-1105103-100340 ; https://digitalcommons.lsu.edu/gradschool_dissertations/346
5.
Ruchlin, Ian.
Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin.
Degree: PhD, School of Physics and Astronomy (COS), 2015, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/8797
► This dissertation explores numerical models of the orbit, inspiral, and merger phases of black hole binaries. We focus on the astrophysically realistic case of…
(more)
▼ This dissertation explores
numerical models of the orbit, inspiral, and merger phases of black hole binaries. We focus on the astrophysically realistic case of black holes with nearly extremal spins, and on high energy black hole collisions. To study the evolution of such systems, we form puncture initial data by solving the four general
relativity constraint equations using pseudospectral methods on a compactified collocation point domain. The solutions to these coupled, nonlinear, elliptic differential equations represent the desired configuration at an initial moment. They are then propagated forward through time using a set of hyperbolic evolution equations with the moving punctures approach in the BSSNOK and CCZ4 formalisms. To generate realistic initial data with reduced spurious gravitational wave content, the background ansatz is taken to be a conformal superposition of Schwarzschild or Kerr spatial metrics. We track the punctures during evolution, measure their horizon properties, extract the gravitational waveforms, and examine the merger remnant. These new initial data are compared with the well known Bowen-York solutions, producing up to an order of magnitude reduction in the initial unphysical gravitational radiation signature. We perform a collision from rest of two black holes with spins near to the extremal value, in a region of parameter space inaccessible to Bowen-York initial data. We simulate nonspinning black holes in quasi-circular orbits, and perform high energy head-on collisions of nonspinning black holes to estimate the magnitude of the radiated gravitational energy in the limit of infinite momentum. We also evolve spinning black holes in quasi-circular orbits with unequal masses and different spin orientations. These models provide insight into the dynamics and signals generated by compact binary systems. This is crucial to our understanding of many astrophysical phenomena, especially to the interpretation of gravitational waves, which are expected to be detected directly for the first time within the next few years.
Advisors/Committee Members: Carlos O. Lousto.
Subjects/Keywords: Black hole; Evolution; General relativity; Initial data; Numerical relativity; Spin
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APA ·
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APA (6th Edition):
Ruchlin, I. (2015). Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin. (Doctoral Dissertation). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/8797
Chicago Manual of Style (16th Edition):
Ruchlin, Ian. “Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin.” 2015. Doctoral Dissertation, Rochester Institute of Technology. Accessed March 01, 2021.
https://scholarworks.rit.edu/theses/8797.
MLA Handbook (7th Edition):
Ruchlin, Ian. “Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin.” 2015. Web. 01 Mar 2021.
Vancouver:
Ruchlin I. Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin. [Internet] [Doctoral dissertation]. Rochester Institute of Technology; 2015. [cited 2021 Mar 01].
Available from: https://scholarworks.rit.edu/theses/8797.
Council of Science Editors:
Ruchlin I. Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin. [Doctoral Dissertation]. Rochester Institute of Technology; 2015. Available from: https://scholarworks.rit.edu/theses/8797
6.
Cook, William.
Numerical relativity in higher dimensional spacetimes.
Degree: PhD, 2018, University of Cambridge
URL: https://doi.org/10.17863/CAM.25057
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999
► The study of general relativity in higher dimensions has proven to be a fruitful avenue of research, revealing new applications of the theory, for instance…
(more)
▼ The study of general relativity in higher dimensions has proven to be a fruitful avenue of research, revealing new applications of the theory, for instance in understanding strongly coupled quantum field theories through the holographic principle, and proposing an explanation of the hierarchy problem through TeV gravity scenarios. To understand the non-linear regime of higher dimensional general relativity, such as that involved in the merger of black holes, we use numerical relativity to solve the Einstein equations. In this thesis we develop and demonstrate several diagnostic tools and new initial data for use in numerical relativity simulations of higher dimensional spacetimes, and use these to investigate binary black hole systems. Firstly, we present a formalism for calculating the gravitational waves in a numerical simulation of a higher dimensional spacetime, and apply this formalism to the example of the head on merger of two equal mass black holes. In doing so, we simulate the merger of black holes in up to 10 spacetime dimensions for the first time, and investigate the dependence of the energy radiated away in gravitational waves on the number of dimensions. We also apply this formalism to the example of head on unequal mass black hole collisions, investigating the dependence of radiated energy and momentum on the number of dimensions and the mass ratio. This study complements and sheds further light on previous work on the merger of point particles with black holes in higher dimensions, and presents evidence for a link between the regime studied, and the large D regime of general relativity where D is the number of spacetime dimensions. We also present initial data that enables us to study black holes with initial momentum and angular momentum, putting in place the framework needed to study problems such as the scattering cross section of black holes in higher dimensions, and the nature of black hole orbits in higher dimensions. Finally, we present, and demonstrate the use of, an apparent horizon finder for higher dimensional spacetimes. This allows us to calculate a black hole's mass and spin, which characterise the black hole.
Subjects/Keywords: 523.8; General Relativity; Numerical Relativity; Black Holes; Higher Dimensions
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APA ·
Chicago ·
MLA ·
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APA (6th Edition):
Cook, W. (2018). Numerical relativity in higher dimensional spacetimes. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.25057 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999
Chicago Manual of Style (16th Edition):
Cook, William. “Numerical relativity in higher dimensional spacetimes.” 2018. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.25057 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999.
MLA Handbook (7th Edition):
Cook, William. “Numerical relativity in higher dimensional spacetimes.” 2018. Web. 01 Mar 2021.
Vancouver:
Cook W. Numerical relativity in higher dimensional spacetimes. [Internet] [Doctoral dissertation]. University of Cambridge; 2018. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.25057 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999.
Council of Science Editors:
Cook W. Numerical relativity in higher dimensional spacetimes. [Doctoral Dissertation]. University of Cambridge; 2018. Available from: https://doi.org/10.17863/CAM.25057 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999
University of Cambridge
7.
Rosca-Mead, Roxana.
Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity.
Degree: PhD, 2019, University of Cambridge
URL: https://doi.org/10.17863/CAM.53747
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810065
► Since the upgrade of the two LIGO Detectors it has been an exciting time for General Relativity (GR) research, as soon after they were upgraded…
(more)
▼ Since the upgrade of the two LIGO Detectors it has been an exciting time for General Relativity (GR) research, as soon after they were upgraded to advanced status GW150914, the first gravitational wave signal from the inspiral and merger of two black holes was detected. The following consistent detections (9 further black hole binaries and one neutron star system) and the introduction of the European interferometer Virgo, as well as other planned detectors such as KAGRA and IndiGO mark the start of a new era of Gravitational Wave Physics and Astrophysics. This provides us with a window into the dynamics of strong gravity as well as the opportunity to test modified gravity and alternative theories in the strong regime, by confirming deviations from GR or constraining such theories. Why is General Relativity not enough though? It has passed all the tests so far with flying colors; in addition, the gravitational waves detected so far have demonstrated excellent agreement with GR’s predictions. Despite all these successful tests, there are still important questions related to Dark Energy and Dark Matter left unexplained. As a consequence, a clearer understanding of modified gravity theories is needed as well as a catalogue of gravitational waves resulting from these theories that could be used in the analysis of interferometer data and for stochastic background and continuous wave searches. In this Thesis we provide source modelling for GR and one of the most popular candidates for modified gravity, Scalar Tensor (ST) theories, as well as look for smoking-gun signatures. We analyse the formation of compact objects from core collapse simulations of stars in massive ST theories over the astrophysically plausible range of stellar progenitor masses and metallicities, as well as a large part of the parameter space of this class of modified theories of gravity. Next we test the robustness of our results by expanding the simulations to ST theories with self-interacting potentials. Finally, we study the recoil resulting from black holes mergers by varying the orbital eccentricity in an attempt to amplify the kicks.
Subjects/Keywords: General Relativity; Modified gravity; Core collapse; Gravitational waves; Numerical relativity
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Record Details
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Rosca-Mead, R. (2019). Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.53747 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810065
Chicago Manual of Style (16th Edition):
Rosca-Mead, Roxana. “Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity.” 2019. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.53747 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810065.
MLA Handbook (7th Edition):
Rosca-Mead, Roxana. “Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity.” 2019. Web. 01 Mar 2021.
Vancouver:
Rosca-Mead R. Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.53747 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810065.
Council of Science Editors:
Rosca-Mead R. Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://doi.org/10.17863/CAM.53747 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810065
Georgia Tech
8.
Ferguson, Deborah Lynn.
Strong-Field Numerical Relativity in the Era of Gravitational Wave Astronomy.
Degree: PhD, Physics, 2020, Georgia Tech
URL: http://hdl.handle.net/1853/64146
► The success of numerical relativity and gravitational wave detectors have paired to provide us with the opportunity to study Einstein’s theory of general relativity in…
(more)
▼ The success of
numerical relativity and gravitational wave detectors have paired to provide us with the opportunity to study Einstein’s theory of general
relativity in the strongest gravitational regimes. With future detectors coming online with higher sensitivities,
numerical relativity will need to continue to improve alongside the detectors. This dissertation addresses how
numerical relativity can be used and improved to obtain the most scientific return from each gravitational wave observation. I first develop a new technique to use
numerical relativity to better characterize the signals from current generation detectors by predicting the spin of the remnant black hole us- ing only the information available from the gravitational wave during merger, the loudest part of a binary black hole coalescence. This gives a way of more accurately characterizing the remnant black hole when very little inspiral is observed, and provides a new general
relativity consistency test using the remnant spin determined from each stage of the coalescence. I then shift my focus towards preparing
numerical relativity to detect and understand signals from next generation grav- itational wave detectors which will be much more sensitive with unique data analysis challenges. In order to produce waveform templates which are indistinguishable from true signals,
numerical relativity simulations will need to be sufficiently well resolved. I construct a method to determine the necessary resolution of
numerical relativity simulations as a function of signal-to-noise ratio. To accurately characterize gravitational wave signals, it is also crucial that the parameter space of binary black hole systems be densely populated with simulations. However, due to the high computational cost of
numerical relativity, these simulations need to be chosen carefully. I develop methods to decrease the effective parameter space and to identify the optimal parameters for new simulations. The methods and techniques presented here help to maximize the scientific gain from each gravitational wave detection, for both present and future detectors.
Advisors/Committee Members: Shoemaker, Deirdre (advisor), Bogdanovic, Tamara (committee member), Cadonati, Laura (committee member), Laguna, Pablo (committee member), Wise, John (committee member).
Subjects/Keywords: Numerical relativity; General relativity; Gravity; Gravitational waves; Black holes
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APA (6th Edition):
Ferguson, D. L. (2020). Strong-Field Numerical Relativity in the Era of Gravitational Wave Astronomy. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/64146
Chicago Manual of Style (16th Edition):
Ferguson, Deborah Lynn. “Strong-Field Numerical Relativity in the Era of Gravitational Wave Astronomy.” 2020. Doctoral Dissertation, Georgia Tech. Accessed March 01, 2021.
http://hdl.handle.net/1853/64146.
MLA Handbook (7th Edition):
Ferguson, Deborah Lynn. “Strong-Field Numerical Relativity in the Era of Gravitational Wave Astronomy.” 2020. Web. 01 Mar 2021.
Vancouver:
Ferguson DL. Strong-Field Numerical Relativity in the Era of Gravitational Wave Astronomy. [Internet] [Doctoral dissertation]. Georgia Tech; 2020. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1853/64146.
Council of Science Editors:
Ferguson DL. Strong-Field Numerical Relativity in the Era of Gravitational Wave Astronomy. [Doctoral Dissertation]. Georgia Tech; 2020. Available from: http://hdl.handle.net/1853/64146
University of Cambridge
9.
Rosca-Mead, Roxana.
Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity.
Degree: PhD, 2019, University of Cambridge
URL: https://www.repository.cam.ac.uk/handle/1810/306660
► Since the upgrade of the two LIGO Detectors it has been an exciting time for General Relativity (GR) research, as soon after they were upgraded…
(more)
▼ Since the upgrade of the two LIGO Detectors it has been an exciting time for General Relativity (GR) research, as soon after they were upgraded to advanced status GW150914, the first gravitational wave signal from the inspiral and merger of two black holes was detected. The following consistent detections (9 further black hole binaries and one neutron star system) and the introduction of the European interferometer Virgo, as well as other planned detectors such as KAGRA and IndiGO mark the start of a new era of Gravitational Wave Physics and Astrophysics. This provides us with a window into the dynamics of strong gravity as well as the opportunity to test modified gravity and alternative theories in the strong regime, by confirming deviations from GR or constraining such theories. Why is General Relativity not enough though? It has passed all the tests so far with flying colors; in addition, the gravitational waves detected so far have demonstrated excellent agreement with GR’s predictions. Despite all these successful tests, there are still important questions related to Dark Energy and Dark Matter left unexplained. As a consequence, a clearer understanding of modified gravity theories is needed as well as a catalogue of gravitational waves resulting from these theories that could be used in the analysis of interferometer data and for stochastic background and continuous wave searches. In this Thesis we provide source modelling for GR and one of the most popular candidates for modified gravity, Scalar Tensor (ST) theories, as well as look for smoking-gun signatures. We analyse the formation of compact objects from core collapse simulations of stars in massive ST theories over the astrophysically plausible range of stellar progenitor masses and metallicities, as well as a large part of the parameter space of this class of modified theories of gravity. Next we test the robustness of our results by expanding the simulations to ST theories with self-interacting potentials. Finally, we study the recoil resulting from black holes mergers by varying the orbital eccentricity in an attempt to amplify the kicks.
Subjects/Keywords: General Relativity; Modified gravity; Core collapse; Gravitational waves; Numerical relativity
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APA (6th Edition):
Rosca-Mead, R. (2019). Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/306660
Chicago Manual of Style (16th Edition):
Rosca-Mead, Roxana. “Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity.” 2019. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://www.repository.cam.ac.uk/handle/1810/306660.
MLA Handbook (7th Edition):
Rosca-Mead, Roxana. “Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity.” 2019. Web. 01 Mar 2021.
Vancouver:
Rosca-Mead R. Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Mar 01].
Available from: https://www.repository.cam.ac.uk/handle/1810/306660.
Council of Science Editors:
Rosca-Mead R. Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://www.repository.cam.ac.uk/handle/1810/306660
Rochester Institute of Technology
10.
Sadiq, Jam.
Analyzing Binary Black hole Spacetimes.
Degree: PhD, School of Physics and Astronomy (COS), 2019, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/10127
► With the first ever detection of gravitational waves from merging black-hole binaries by LIGO (Laser Interferometer GravitationalWave Observatory), a new era of gravitational wave…
(more)
▼ With the first ever detection of gravitational waves from merging black-hole binaries by LIGO (Laser Interferometer GravitationalWave Observatory), a new era of gravitational wave astronomy was started. With its increased sensitivity, LIGO will see many more black-hole binaries in the future. To detect the gravitational waves and elucidate the properties of their sources, one needs theoretical waveform templates. These, in turn, require solving Einstein field equations, at least approximately. Approximate techniques like post-Newtonian theory and black-hole perturbation theory can produce waveforms that are accurate for certain phases of binaries evolution.
Numerical relativity, on the other hand, can in principle produce accurate waveforms models for the full binary evolution. However, such simulations are computationally very expensive for the slow inspiral phase. To overcome this issue, we hybridized
numerical relativity obtained by solving the Einstein field equations during the late-inspiral, plunge, and ringdown phase and post-Newtonian waveforms for the early-inspiral phase. Here we focus on hybridizing waveforms for precessing black-hole binaries. In this work we also developed a new tool to test the accuracy limits of approximate a binary black-hole spacetimes constructed using analytical approximate techniques. Our method is based on direct comparison to a numerically generated solution to the Einstein field equations.
Advisors/Committee Members: David Ross.
Subjects/Keywords: Black holes; Gravitational waves; Numerical relativity
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APA (6th Edition):
Sadiq, J. (2019). Analyzing Binary Black hole Spacetimes. (Doctoral Dissertation). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/10127
Chicago Manual of Style (16th Edition):
Sadiq, Jam. “Analyzing Binary Black hole Spacetimes.” 2019. Doctoral Dissertation, Rochester Institute of Technology. Accessed March 01, 2021.
https://scholarworks.rit.edu/theses/10127.
MLA Handbook (7th Edition):
Sadiq, Jam. “Analyzing Binary Black hole Spacetimes.” 2019. Web. 01 Mar 2021.
Vancouver:
Sadiq J. Analyzing Binary Black hole Spacetimes. [Internet] [Doctoral dissertation]. Rochester Institute of Technology; 2019. [cited 2021 Mar 01].
Available from: https://scholarworks.rit.edu/theses/10127.
Council of Science Editors:
Sadiq J. Analyzing Binary Black hole Spacetimes. [Doctoral Dissertation]. Rochester Institute of Technology; 2019. Available from: https://scholarworks.rit.edu/theses/10127
Rochester Institute of Technology
11.
Lange, Jacob A.
Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation.
Degree: MS, School of Physics and Astronomy (COS), 2016, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/9323
► We compare real and synthetic data directly to complete numerical relativity simulations of binary black holes. Even though our method largely agrees with ,…
(more)
▼ We compare real and synthetic data directly to complete
numerical relativity simulations of binary black holes. Even though our method largely agrees with , our method goes beyond the existing semi-analytic models that were used. Comparisons with only the quadrupole modes constrain the redshifted mass M
z∈[64 M
\bigodot-82 M
\bigodot], mass ratio 1/q=m
2/m
1∈[0.6,1], effective aligned spin χ
eff∈[-0.3,0.2], where χ
eff=(\mathbf{S}
1/m
1+\mathbf{S
2}/m
2)∙\mathbf{L̂}/M. If we include the octopole modes, we can constrain the mass ratio even better. Even though the spins are correlated, both magnitude and directions are not significantly constrained by the data. We determine that an upper limit for the spin magnitudes up to at least 0.8 but with random orientations. When we interpolate between nonprecessing binaries and reconstruct the posterior distribution, we find it is consistent with the results in . We found a final total black hole redshifted mass is consistent with M
f,z in the range 64.0 M
\bigodot-73.5 M
\bigodot, and we found a final dimensionless spin parameter to be constrained to a
f=0.62-0.73. To better understand and quantify the impact of potential sources of error, we calculated mismatches between waveforms and the KL Divergence(D
KL) between PDFs derived from fits to our \lnLmarg from our it{integrate\
likelihood\
extrinsic} code (called it{ILE}). The error due to Monte Carlo integration was found to have a insignificant effect on the PDFs giving D
KL∼10
-5. The impact of extracting the waveform was also found to be minimal assuming a high enough extraction radius is possible; we found D
KL∼10
-2-10
-3 for PDFs corresponding to sources with different extraction radii. The resolution of a simulation was also found to have an extremely low impact with D
KL∼10
-4. Our most noticeable source of error was the low frequency cutoffs, which produced D
KL∼2 for two PDFs with the biggest differences; however, this effect becomes less significant after marginalizing over all dimensions. We also use different sources for three end-to-end runs: zero spin, equal mass; aligned spin, unequal mass; and precessing, unequal mass. For all three cases, we were able to constrain the same parameters as with the analysis of the real event. For all three cases, the true system parameters lied within our reconstructed posterior. For the aligned case, we ran comparisons using the octopole modes and found, as in the real event analyses, we could further constrain the mass ratio.
Advisors/Committee Members: Richard O’Shaughnessy.
Subjects/Keywords: Binary black holes; Gravitational waves; Numerical relativity
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APA (6th Edition):
Lange, J. A. (2016). Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation. (Masters Thesis). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/9323
Chicago Manual of Style (16th Edition):
Lange, Jacob A. “Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation.” 2016. Masters Thesis, Rochester Institute of Technology. Accessed March 01, 2021.
https://scholarworks.rit.edu/theses/9323.
MLA Handbook (7th Edition):
Lange, Jacob A. “Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation.” 2016. Web. 01 Mar 2021.
Vancouver:
Lange JA. Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation. [Internet] [Masters thesis]. Rochester Institute of Technology; 2016. [cited 2021 Mar 01].
Available from: https://scholarworks.rit.edu/theses/9323.
Council of Science Editors:
Lange JA. Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation. [Masters Thesis]. Rochester Institute of Technology; 2016. Available from: https://scholarworks.rit.edu/theses/9323
12.
Hemberger, Daniel.
Numerical Evolutions Of Binary Black Hole Systems.
Degree: PhD, Astronomy, 2013, Cornell University
URL: http://hdl.handle.net/1813/34160
Subjects/Keywords: numerical relativity
…phenomenological waveform
models are used. These models are calibrated using numerical relativity results… …Because of the limited
number of numerical relativity waveforms, these phenomenological… …Cook, and Saul A. Teukolsky. High-accuracy
comparison of numerical relativity simulations… …postNewtonian/numerical-relativity hybrid waveforms for gravitational wave detectors. Class.
Quantum… …numerical relativity - status of complete gravitational
waveform models for binary black holes…
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APA (6th Edition):
Hemberger, D. (2013). Numerical Evolutions Of Binary Black Hole Systems. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/34160
Chicago Manual of Style (16th Edition):
Hemberger, Daniel. “Numerical Evolutions Of Binary Black Hole Systems.” 2013. Doctoral Dissertation, Cornell University. Accessed March 01, 2021.
http://hdl.handle.net/1813/34160.
MLA Handbook (7th Edition):
Hemberger, Daniel. “Numerical Evolutions Of Binary Black Hole Systems.” 2013. Web. 01 Mar 2021.
Vancouver:
Hemberger D. Numerical Evolutions Of Binary Black Hole Systems. [Internet] [Doctoral dissertation]. Cornell University; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1813/34160.
Council of Science Editors:
Hemberger D. Numerical Evolutions Of Binary Black Hole Systems. [Doctoral Dissertation]. Cornell University; 2013. Available from: http://hdl.handle.net/1813/34160
Georgia Tech
13.
Clark, Michael C.
Bowen-type initial data for simulations of neutron stars in binary systems.
Degree: PhD, Physics, 2016, Georgia Tech
URL: http://hdl.handle.net/1853/55005
► A new method for generating initial data for simulations of neutron stars in binary systems. The construction of physically relevant initial data is crucial to…
(more)
▼ A new method for generating initial data for simulations of neutron stars in binary systems. The construction of physically relevant initial data is crucial to accurate assessment of gravitational wave signals relative to theoretical predictions. This method builds upon the Bowen-York curvature for puncture black holes. This data is evolved and compared against simulations in the literature with respect to orbital eccentricity, merger and collapse times, and emitted energy and angular momentum. The data exhibits some defects, including large central density oscillations in stars and center of mass drift in unequal-mass systems. Some approaches for improvements in potential future work are discussed.
Advisors/Committee Members: Wise, John (advisor), Laguna, Pablo (committee member), Shoemaker, Deirdre (committee member), Cadonati, Laura (committee member), Bader, David (committee member).
Subjects/Keywords: Numerical relativity; Astrophysics; Neutron stars; Gravitational waves
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APA (6th Edition):
Clark, M. C. (2016). Bowen-type initial data for simulations of neutron stars in binary systems. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/55005
Chicago Manual of Style (16th Edition):
Clark, Michael C. “Bowen-type initial data for simulations of neutron stars in binary systems.” 2016. Doctoral Dissertation, Georgia Tech. Accessed March 01, 2021.
http://hdl.handle.net/1853/55005.
MLA Handbook (7th Edition):
Clark, Michael C. “Bowen-type initial data for simulations of neutron stars in binary systems.” 2016. Web. 01 Mar 2021.
Vancouver:
Clark MC. Bowen-type initial data for simulations of neutron stars in binary systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1853/55005.
Council of Science Editors:
Clark MC. Bowen-type initial data for simulations of neutron stars in binary systems. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/55005
Leiden University
14.
Sterk, Peter.
Formation of black branes with U(1) scalar hair.
Degree: 2017, Leiden University
URL: http://hdl.handle.net/1887/52788
► We describe a complete strategy to numerically compute the collapse of a massless U(1) charged scalar field into a black brane final state in 4+1-dimensional…
(more)
▼ We describe a complete strategy to numerically compute the collapse of a massless U(1) charged scalar field into a black brane final state in 4+1-dimensional anti-de Sitter space. We implement this strategy to investigate the formation of scalar hair, corresponding to a superconducting order parameter in a dual conformal field theory. We show that the approach to the final state takes the form of damped oscillations, with the degree of damping being strongly dependent on the temperature of the final state, as well as on the near-boundary shape of the initial distribution.
Advisors/Committee Members: Schalm, Koenraad (advisor).
Subjects/Keywords: numerical general relativity; numerical relativity; general relativity; AdS/CFT; black brane; black hole; scalar field; Reissner-Nordström; holographic superconductor
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APA (6th Edition):
Sterk, P. (2017). Formation of black branes with U(1) scalar hair. (Masters Thesis). Leiden University. Retrieved from http://hdl.handle.net/1887/52788
Chicago Manual of Style (16th Edition):
Sterk, Peter. “Formation of black branes with U(1) scalar hair.” 2017. Masters Thesis, Leiden University. Accessed March 01, 2021.
http://hdl.handle.net/1887/52788.
MLA Handbook (7th Edition):
Sterk, Peter. “Formation of black branes with U(1) scalar hair.” 2017. Web. 01 Mar 2021.
Vancouver:
Sterk P. Formation of black branes with U(1) scalar hair. [Internet] [Masters thesis]. Leiden University; 2017. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1887/52788.
Council of Science Editors:
Sterk P. Formation of black branes with U(1) scalar hair. [Masters Thesis]. Leiden University; 2017. Available from: http://hdl.handle.net/1887/52788
University of Toronto
15.
Lewis, Adam Gabriel Marcel.
Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations.
Degree: PhD, 2018, University of Toronto
URL: http://hdl.handle.net/1807/89684
► Numerical relativity, the direct numerical integration of the Einstein field equations, is now a mature subfield of computational physics, playing a critical role in the…
(more)
▼ Numerical relativity, the direct
numerical integration of the Einstein field equations, is now a mature subfield of computational physics, playing a critical role in the generation of signal templates for comparison with data from ground-based gravitational wave detectors. The application of
numerical relativity techniques to new problems is at present complicated by long wallclock times and intricate code. In this thesis we lay groundwork to improve this situation by presenting a GPU port of the
numerical relativity code SpEC. Our port keeps code maintenance feasible by relying on various layers of automation, and achieves high performance across a variety of GPUs. We secondly introduce a C++ software package, TLoops, which allows
numerical manipulation of tensors using single-line C++ source-code expressions resembling familiar tensor calculus notation. These expressions may be compiled and executed immediately, but also can be used to automatically generate equivalent GPU or low-level CPU code, which then executes in their place. The GPU code in particular achieves near-peak performance. Finally, we present simulations of eccentric binary black holes. We develop new methods to extract the fundamental frequencies of these systems. Using these frequencies we identify when these binaries pass through coordinate resonances, at which points high mass-ratio inspirals can experience short-timescale phase-dependent deviations from smooth inspiral called "kicks". We find no evidence for such kicks at comparable mass-ratio.
Advisors/Committee Members: Pfeiffer, Harald P., Physics.
Subjects/Keywords: Binary black holes; Black holes; CUDA; General relativity; GPU; Numerical relativity; 0605
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APA (6th Edition):
Lewis, A. G. M. (2018). Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/89684
Chicago Manual of Style (16th Edition):
Lewis, Adam Gabriel Marcel. “Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations.” 2018. Doctoral Dissertation, University of Toronto. Accessed March 01, 2021.
http://hdl.handle.net/1807/89684.
MLA Handbook (7th Edition):
Lewis, Adam Gabriel Marcel. “Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations.” 2018. Web. 01 Mar 2021.
Vancouver:
Lewis AGM. Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations. [Internet] [Doctoral dissertation]. University of Toronto; 2018. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1807/89684.
Council of Science Editors:
Lewis AGM. Orbital Resonances and GPU Acceleration of Binary Black Hole Inspiral Simulations. [Doctoral Dissertation]. University of Toronto; 2018. Available from: http://hdl.handle.net/1807/89684
Georgia Tech
16.
Kinsey, Matthew Christopher.
General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity.
Degree: PhD, Physics, 2016, Georgia Tech
URL: http://hdl.handle.net/1853/55557
► With the recent first detection of gravitational waves, numerical relativity provides us with the most promising tools of astronomical discovery, particularly for strong dynamical gravity…
(more)
▼ With the recent first detection of gravitational waves,
numerical relativity provides us with the most promising tools of astronomical discovery, particularly for strong dynamical gravity phenomena where analytic solutions remain elusive. However, finding
numerical solutions to the Einstein field equations of General
Relativity and their accompanying matter source equations often comes at a steep computational cost. In this thesis, I present a Lagrangian formalism for solving the equations of relativistic hydrodynamics in a dynamical 3+1 spacetime using `smoothed particle hydrodynamics' (SPH) techniques. This method comes with numerous advantages over more traditional Eulerian methods. In particular, the resolution of SPH naturally follows the density distribution of the fluid: a distribution that may span many orders of magnitude in relevant astrophysical problems. The accuracy and validity of this method is then established by showing agreement with well-established analytical test cases in relativistic hydrodynamics. Additionally, I highlight the parallel properties of this method and discuss how this approach naturally lends itself well to a scientific computing environment that is increasingly seeing gains, not from higher clock rates, but rather a push towards massive parallelism.
Advisors/Committee Members: Wise, John H (advisor), Laguna, Pablo (committee member), Shoemaker, Deirdre M (committee member), Bogdanovic, Tamara (committee member), Vuduc, Richard (committee member).
Subjects/Keywords: Numerical Relativity; Hydrodynamics; General Relativity; Smoothed Particle Hydrodynamics; Hierarchical Spatial Hashing; Parallel Computing
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APA (6th Edition):
Kinsey, M. C. (2016). General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/55557
Chicago Manual of Style (16th Edition):
Kinsey, Matthew Christopher. “General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity.” 2016. Doctoral Dissertation, Georgia Tech. Accessed March 01, 2021.
http://hdl.handle.net/1853/55557.
MLA Handbook (7th Edition):
Kinsey, Matthew Christopher. “General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity.” 2016. Web. 01 Mar 2021.
Vancouver:
Kinsey MC. General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1853/55557.
Council of Science Editors:
Kinsey MC. General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/55557
University of Maryland
17.
Boggs, William Darian.
Novel Techniques for Simulation and Analysis of Black Hole Mergers.
Degree: Physics, 2011, University of Maryland
URL: http://hdl.handle.net/1903/11726
► This dissertation consists of three research topics from numerical relativity: waveforms from inspiral mergers of black hole binaries, recoils from head-on mergers of black holes,…
(more)
▼ This dissertation consists of three research topics from
numerical relativity: waveforms from inspiral mergers of black hole binaries, recoils from head-on mergers of black holes, and a new computational technique for error-reduction. The first two topics present research from journal articles that I coauthored with my colleagues in the NASA Goddard
Numerical Relativity research group.
Chapter 2 discusses a heuristic model of black hole binary mergers and the waveforms produced by them, based on simulations of nonspinning black holes. The gravitational radiation is interpreted as the result of an implicit rotating source that generates the radiation modes as the source multipoles rotate coherently. This interpretation of the waveform phase evolution provides a unified physical picture of the inspiral, plunge, and ringdown of the binaries, and it is the basis of an analytic model of the late-time frequency evolution.
Chapter 3 presents a study of kicks in head-on black hole mergers, emphasizing the distinct contributions of spin and mass ratio, as well as their combined effects,
to these radiation-induced recoils. The simpler dynamics of head-on mergers allow a more clear separation of the two types of kick and a validation of post-Newtonian predictions for the spin scaling of kicks.
Finally, Chapter 4 presents a technique I developed to improve the accuracy of the field evolution in
numerical relativity simulations. This "moving patches" technique uses local coordinate frames to minimize black hole motion and reduce error due to advection terms. In tests of the technique, I demonstrate reduction in constraint violations and in errors in the orbital frequency derived from the black holes' motions. I also demonstrate an accuracy gain in a new diagnostic quantity based on orbital angular momentum. I developed this diagnostic for evaluating the moving patches technique, but it has broader applicability. Though the moving patches technique has significant performance costs, these limitations are specific to the current implementation, and it promises greater efficiency and accuracy in the future.
Advisors/Committee Members: Tiglio, Manuel (advisor).
Subjects/Keywords: Astrophysics; Theoretical Physics; black hole; computational physics; general relativity; gravitational wave; gravity; numerical relativity
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APA (6th Edition):
Boggs, W. D. (2011). Novel Techniques for Simulation and Analysis of Black Hole Mergers. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/11726
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Boggs, William Darian. “Novel Techniques for Simulation and Analysis of Black Hole Mergers.” 2011. Thesis, University of Maryland. Accessed March 01, 2021.
http://hdl.handle.net/1903/11726.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Boggs, William Darian. “Novel Techniques for Simulation and Analysis of Black Hole Mergers.” 2011. Web. 01 Mar 2021.
Vancouver:
Boggs WD. Novel Techniques for Simulation and Analysis of Black Hole Mergers. [Internet] [Thesis]. University of Maryland; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1903/11726.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Boggs WD. Novel Techniques for Simulation and Analysis of Black Hole Mergers. [Thesis]. University of Maryland; 2011. Available from: http://hdl.handle.net/1903/11726
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Cambridge
18.
Crisford, Toby.
Violating the weak cosmic censorship conjecture in asymptotically Anti-de Sitter space-times.
Degree: PhD, 2019, University of Cambridge
URL: https://doi.org/10.17863/CAM.46123
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.793129
► We numerically construct solutions to four dimensional General Relativity with negative cosmological constant, both with and without an electromagnetic field. Our results suggest that in…
(more)
▼ We numerically construct solutions to four dimensional General Relativity with negative cosmological constant, both with and without an electromagnetic field. Our results suggest that in both cases the space-time curvature can be made to grow without bound in a region visible to distant observers by imposing sufficiently violent boundary conditions on the metric or gauge field. In the electromagnetic case, this only happens at zero temperature, and we present a new numerical scheme capable of performing time evolution in this context. We argue that our results, at least in the electromagnetic case, violate the spirit of the Weak Cosmic Censorship Conjecture, so that this conjecture fails in 3+ 1 dimensional asymptotically Anti de-Sitter spaces. We then argue that if charged fields are included with a sufficiently large charge relative to their mass, cosmic censorship appears to be restored. The minimal charge agrees precisely with the bound given by the Weak Gravity Conjecture, suggesting an intriguing connection between this conjecture and cosmic censorship. More generally, we propose that "large" naked singularities, where the curvature becomes large over a large region of space, will be forbidden in any theory which can be completed into quantum gravity in the UV.
Subjects/Keywords: General Relativity; Cosmic Censorship; Weak Gravity Conjecture; Anti-de Sitter Space; Numerical Relativity
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APA (6th Edition):
Crisford, T. (2019). Violating the weak cosmic censorship conjecture in asymptotically Anti-de Sitter space-times. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.46123 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.793129
Chicago Manual of Style (16th Edition):
Crisford, Toby. “Violating the weak cosmic censorship conjecture in asymptotically Anti-de Sitter space-times.” 2019. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.46123 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.793129.
MLA Handbook (7th Edition):
Crisford, Toby. “Violating the weak cosmic censorship conjecture in asymptotically Anti-de Sitter space-times.” 2019. Web. 01 Mar 2021.
Vancouver:
Crisford T. Violating the weak cosmic censorship conjecture in asymptotically Anti-de Sitter space-times. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.46123 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.793129.
Council of Science Editors:
Crisford T. Violating the weak cosmic censorship conjecture in asymptotically Anti-de Sitter space-times. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://doi.org/10.17863/CAM.46123 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.793129
University of Cambridge
19.
Kunesch, Markus.
Numerical simulations of instabilities in general relativity.
Degree: PhD, 2018, University of Cambridge
URL: https://doi.org/10.17863/CAM.30498
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593
► General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time…
(more)
▼ General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time for more than 100 years and has passed all experimental tests so far. Most recently, the LIGO collaboration made the first-ever direct detection of gravitational waves, confirming a long-standing prediction of general relativity. Despite this, several fundamental mathematical questions remain unanswered, many of which relate to the global existence and the stability of solutions to Einstein's equations. This thesis presents our efforts to use numerical relativity to investigate some of these questions. We present a complete picture of the end points of black ring instabilities in five dimensions. Fat rings collapse to Myers-Perry black holes. For intermediate rings, we discover a previously unknown instability that stretches the ring without changing its thickness and causes it to collapse to a Myers-Perry black hole. Most importantly, however, we find that for very thin rings, the Gregory-Laflamme instability dominates and causes the ring to break. This provides the first concrete evidence that in higher dimensions, the weak cosmic censorship conjecture may be violated even in asymptotically flat spacetimes. For Myers-Perry black holes, we investigate instabilities in five and six dimensions. In six dimensions, we demonstrate that both axisymmetric and non-axisymmetric instabilities can cause the black hole to pinch off, and we study the approach to the naked singularity in detail. Another question that has attracted intense interest recently is the instability of anti-de Sitter space. In this thesis, we explore how breaking spherical symmetry in gravitational collapse in anti-de Sitter space affects black hole formation. These findings were made possible by our new open source general relativity code, GRChombo, whose adaptive mesh capabilities allow accurate simulations of phenomena in which new length scales are produced dynamically. In this thesis, we describe GRChombo in detail, and analyse its performance on the latest supercomputers. Furthermore, we outline numerical advances that were necessary for simulating higher dimensional black holes stably and efficiently.
Subjects/Keywords: 523.8; general relativity; black holes; cosmic censorship; numerical relativity; higher dimensions; AdS; adaptive mesh refinement
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APA (6th Edition):
Kunesch, M. (2018). Numerical simulations of instabilities in general relativity. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.30498 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593
Chicago Manual of Style (16th Edition):
Kunesch, Markus. “Numerical simulations of instabilities in general relativity.” 2018. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.30498 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593.
MLA Handbook (7th Edition):
Kunesch, Markus. “Numerical simulations of instabilities in general relativity.” 2018. Web. 01 Mar 2021.
Vancouver:
Kunesch M. Numerical simulations of instabilities in general relativity. [Internet] [Doctoral dissertation]. University of Cambridge; 2018. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.30498 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593.
Council of Science Editors:
Kunesch M. Numerical simulations of instabilities in general relativity. [Doctoral Dissertation]. University of Cambridge; 2018. Available from: https://doi.org/10.17863/CAM.30498 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593
University of Toronto
20.
Woodford, Charles Joseph.
Centre-of-mass Motion and Precession of the Orbital Plane in Black Hole Simulations.
Degree: PhD, 2020, University of Toronto
URL: http://hdl.handle.net/1807/103780
► This work focuses on the inherent gauge ambiguity in general relativity (GR), related gauge effects in numerical relativity (NR), and the extraction of gauge-invariant, observable…
(more)
▼ This work focuses on the inherent gauge ambiguity
in general
relativity (GR), related gauge effects in
numerical relativity (NR), and the
extraction of gauge-invariant, observable measures from NR. Gauge ambiguity is an inescapable feature of GR, analogous to not knowing which reference frame a system is in.
This can create unphysical effects in data from strong gravity regime simulations, which
ultimately become a source of error if not accounted for.
NR involves solving Einstein's equations on a computer. Here, NR is used to obtain
accurate solutions for compact binary systems, namely binary black holes (BBH). BBH are
observed through the emission of gravitational radiation as the binary undergoes inspiral,
merger, and ringdown of the remnant black hole. Gravitational wave (GW)
information from NR is represented as waveforms, typically decomposed into spin-weighted
spherical harmonics, as is the case for the Simulating Extreme Spacetimes (SXS) collaboration.
The first project is an analysis of the centre-of-mass (c.m.) in simulations of BBH. The
c.m. is considered the origin for the decomposed waveforms, and
unphysical movement in the c.m. erroneously affects the reported GWs. We
establish that there is an initial displacement from the origin and a velocity kick that
causes an overall linear drift in the c.m. We develop techniques to characterize, analyze, and
``remove'' effects of c.m. motion on the GWs by transforming the frame of
reference, otherwise known as a gauge-transformation. The resulting GWs
are proven to be more accurate and reliable. The removal of the linear c.m. drift is now a
permanent post-processing step for all simulations in the SXS catalog.
The second project is an investigation into the precession of the orbital plane of
BBH, which is resilient against a larger set of gauge transformations than completely
gauge-dependent quantities and therefore more reliable for comparisons between simulations,
codes, and theories. We compare information extracted from simulations of BBH to
Self-force perturbation theory (SF). The rate of precession of the orbital plane is
extracted from NR and compared with Kerr geodesics, which allowed for the first
and second order SF coefficients to be extracted.
Advisors/Committee Members: Murray, Norman W, Physics.
Subjects/Keywords: Binary Black Holes; Gauge Ambiguity; General Relativity; Gravitational Waves; Numerical Relativity; 0596
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APA (6th Edition):
Woodford, C. J. (2020). Centre-of-mass Motion and Precession of the Orbital Plane in Black Hole Simulations. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/103780
Chicago Manual of Style (16th Edition):
Woodford, Charles Joseph. “Centre-of-mass Motion and Precession of the Orbital Plane in Black Hole Simulations.” 2020. Doctoral Dissertation, University of Toronto. Accessed March 01, 2021.
http://hdl.handle.net/1807/103780.
MLA Handbook (7th Edition):
Woodford, Charles Joseph. “Centre-of-mass Motion and Precession of the Orbital Plane in Black Hole Simulations.” 2020. Web. 01 Mar 2021.
Vancouver:
Woodford CJ. Centre-of-mass Motion and Precession of the Orbital Plane in Black Hole Simulations. [Internet] [Doctoral dissertation]. University of Toronto; 2020. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1807/103780.
Council of Science Editors:
Woodford CJ. Centre-of-mass Motion and Precession of the Orbital Plane in Black Hole Simulations. [Doctoral Dissertation]. University of Toronto; 2020. Available from: http://hdl.handle.net/1807/103780
Rochester Institute of Technology
21.
Munro, Eugene.
Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field.
Degree: MS, School of Mathematical Sciences (COS), 2013, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/9080
► In this paper, we will solve the Hamiltonian constraint describing a curved general relativistic spacetime to find initial data describing how a black hole…
(more)
▼ In this paper, we will solve the Hamiltonian constraint describing a curved general relativistic spacetime to find initial data describing how a black hole exists in vacuum. This has been done before by other researchers [Ansorg, 2004], and we will be adapting our own methods to an existing pseudo spectral Poisson solver [Gourgoulhon, 2001]. The need for this adaptation arises from improper
numerical handling, done by pseudo spectral-methods, of a large part the Hamiltonian constraint equation due to the presence of the black hole singularity. To resolve a portion of this issue up to a given order, we will determine irregularities by executing a polynomial expansion on the Hamiltonian constraint, analytically solving the troublesome components of the equation and subtracting those out of the
numerical process. This technique will increase the equation's differentiability and allow the
numerical solver to run more efficiently.
We will cover all the calculations needed to describe one black hole with arbitrary spin and linear momentum. Our process is easily expanded into cases with
n black holes [Brandt,1997], which we will show in chapter 2. We will implement a spherical harmonic decomposition of the black hole conformal factor, using them as basis functions by which to further expand and dissect the Hamiltonian Constraint equation. In the end, the expansion and subtraction method will be done out to the order of r
4, where
r is the spherical radius assuming the black hole is at the coordinate origin, making the Hamiltonian equation, which, unaltered, is a C
2 equation, become a C
7 equation. Smoothing the Hamiltonian improves
numerical precision, especially near the BH where the most interesting physics occurs. The method used in this paper can be further implemented to higher orders of
r to yield even smoother conditions. We will test the
numerical results of using this method against the existing solver that uses the publicly available Lorene
numerical libraries and programmed in C.
Advisors/Committee Members: Josh A. Faber.
Subjects/Keywords: Black hole; Initial data; Numerical relativity; Pseudo spectral
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APA ·
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MLA ·
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APA (6th Edition):
Munro, E. (2013). Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field. (Masters Thesis). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/9080
Chicago Manual of Style (16th Edition):
Munro, Eugene. “Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field.” 2013. Masters Thesis, Rochester Institute of Technology. Accessed March 01, 2021.
https://scholarworks.rit.edu/theses/9080.
MLA Handbook (7th Edition):
Munro, Eugene. “Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field.” 2013. Web. 01 Mar 2021.
Vancouver:
Munro E. Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field. [Internet] [Masters thesis]. Rochester Institute of Technology; 2013. [cited 2021 Mar 01].
Available from: https://scholarworks.rit.edu/theses/9080.
Council of Science Editors:
Munro E. Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field. [Masters Thesis]. Rochester Institute of Technology; 2013. Available from: https://scholarworks.rit.edu/theses/9080
Rochester Institute of Technology
22.
Silberman, Zachary J.
Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics.
Degree: PhD, School of Physics and Astronomy (COS), 2018, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/9878
► Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalisms, some of these…
(more)
▼ Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalisms, some of these codes evolve the vector potential A, and others evolve the magnetic field B = curl(A) directly. Given that these codes possess unique strengths, it is sometimes desirable to start a simulation using a code that evolves B and complete it using a code that evolves A. Transferring data from one code to another requires an inverse curl algorithm. This dissertation describes two new inverse curl techniques in the context of Cartesian
numerical grids: a cell-by-cell method, which scales approximately linearly with the size of the
numerical grid, and a global linear algebra approach, which lacks those ideal scaling properties but is generally more robust, e.g., in the context of a magnetic field possessing some nonzero divergence. We demonstrate that these algorithms successfully generate smooth vector potential configurations in challenging special and general relativistic contexts. In addition, we examine the magnetic helicity, which is a measure of the overall "twist" of a magnetic field configuration. It is defined as the integral of the dot product of A and B over the volume, and it should be conserved as a system evolves. By examining this quantity, we can put further constraints on the physical accuracy of
numerical codes.
Advisors/Committee Members: Joshua Faber.
Subjects/Keywords: Inverse curl; Magnetic heilcity; Magnetohydrodynamics; Numerical relativity; Vector potential
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APA (6th Edition):
Silberman, Z. J. (2018). Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics. (Doctoral Dissertation). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/9878
Chicago Manual of Style (16th Edition):
Silberman, Zachary J. “Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics.” 2018. Doctoral Dissertation, Rochester Institute of Technology. Accessed March 01, 2021.
https://scholarworks.rit.edu/theses/9878.
MLA Handbook (7th Edition):
Silberman, Zachary J. “Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics.” 2018. Web. 01 Mar 2021.
Vancouver:
Silberman ZJ. Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics. [Internet] [Doctoral dissertation]. Rochester Institute of Technology; 2018. [cited 2021 Mar 01].
Available from: https://scholarworks.rit.edu/theses/9878.
Council of Science Editors:
Silberman ZJ. Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics. [Doctoral Dissertation]. Rochester Institute of Technology; 2018. Available from: https://scholarworks.rit.edu/theses/9878
Cornell University
23.
Foucart, Francois.
Numerical Studies Of Black Hole-Neutron Star Binaries.
Degree: PhD, Physics, 2011, Cornell University
URL: http://hdl.handle.net/1813/30652
► Black hole-neutron star mergers are extremely energetic events with the potential to generate gravitational waves detectable by ground-based detectors. They can also form massive, hot…
(more)
▼ Black hole-neutron star mergers are extremely energetic events with the potential to generate gravitational waves detectable by ground-based detectors. They can also form massive, hot accretion discs around a remnant black hole, which could power short gamma-ray bursts. Due to the strength of the gravitational interactions around the time of merger, black hole-neutron star binaries can only be studied in a general relativistic framework – and as we lack analytical solutions to Einstein's equations of general
relativity in the case of binary systems,
numerical simulations are required to determine their evolution. In this thesis, we study black hole-neutron star binaries using the SpEC code. We show how to efficiently and accurately determine the initial conditions for
numerical simulations, and study the influence on the dynamics of black hole-neutron star mergers of both the equation of state of nuclear matter - which is unknown but could be constrained through observations of compact binaries - and the spin of the black hole. We find that the dynamics of mergers is strongly affected by the radius of the star: small stars are harder to disrupt, form lower-mass discs and emit waves longer (and at higher frequency) than large stars. The component of the black hole spin aligned with the orbital angular momentum of the binary also modifies the disk formation process: high spins let the star approach closer to the black hole without plunging into it, subjecting it to stronger tidal forces and making it easier for the star to disrupt and form a massive disk.
Advisors/Committee Members: Teukolsky, Saul A (chair), Patterson, J Ritchie (committee member), Flanagan, Eanna E (committee member).
Subjects/Keywords: General Relativity; Black Hole-Neutron Star Binaries; Numerical Simulations
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APA (6th Edition):
Foucart, F. (2011). Numerical Studies Of Black Hole-Neutron Star Binaries. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/30652
Chicago Manual of Style (16th Edition):
Foucart, Francois. “Numerical Studies Of Black Hole-Neutron Star Binaries.” 2011. Doctoral Dissertation, Cornell University. Accessed March 01, 2021.
http://hdl.handle.net/1813/30652.
MLA Handbook (7th Edition):
Foucart, Francois. “Numerical Studies Of Black Hole-Neutron Star Binaries.” 2011. Web. 01 Mar 2021.
Vancouver:
Foucart F. Numerical Studies Of Black Hole-Neutron Star Binaries. [Internet] [Doctoral dissertation]. Cornell University; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1813/30652.
Council of Science Editors:
Foucart F. Numerical Studies Of Black Hole-Neutron Star Binaries. [Doctoral Dissertation]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/30652
Cornell University
24.
Henriksson, Katherine.
Topics In Neutron Star Physics.
Degree: PhD, Physics, 2015, Cornell University
URL: http://hdl.handle.net/1813/39369
Subjects/Keywords: Neutron Stars; Superconductivity; Numerical Relativity
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APA (6th Edition):
Henriksson, K. (2015). Topics In Neutron Star Physics. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/39369
Chicago Manual of Style (16th Edition):
Henriksson, Katherine. “Topics In Neutron Star Physics.” 2015. Doctoral Dissertation, Cornell University. Accessed March 01, 2021.
http://hdl.handle.net/1813/39369.
MLA Handbook (7th Edition):
Henriksson, Katherine. “Topics In Neutron Star Physics.” 2015. Web. 01 Mar 2021.
Vancouver:
Henriksson K. Topics In Neutron Star Physics. [Internet] [Doctoral dissertation]. Cornell University; 2015. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1813/39369.
Council of Science Editors:
Henriksson K. Topics In Neutron Star Physics. [Doctoral Dissertation]. Cornell University; 2015. Available from: http://hdl.handle.net/1813/39369
Penn State University
25.
Bentivegna, Eloisa.
Ringing in unison: exploring black hole coalescence with quasinormal modes.
Degree: 2008, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/8245
► The computational modeling of systems in the strong-gravity regime of General Relativity and the extraction of a coherent physical picture from the numerical data is…
(more)
▼ The computational modeling of systems in the strong-gravity
regime of General
Relativity and the extraction of a coherent
physical picture from the
numerical data is a crucial step in
the process of detecting and recognizing the theory's imprint
on our universe. Obtained and consolidated over the past two
years, full 3D simulations of binary black hole systems
in vacuum constitute one of the first successful steps in this
field, based on the synergy of theoretical modeling,
numerical
analysis and computer science efforts.
This dissertation seeks to model the merger of two coalescing
black holes, employing a novel technique consisting of the
propagation of a massless scalar field on the spacetime where the
coalescence is taking place: the field is evolved on a set of
fixed backgrounds, each provided by a spatial hypersurface generated
numerically during a binary black hole merger. The scalar field
scattered from the merger region exhibits quasinormal ringing once
a common apparent horizon surrounds the two black holes. This
occurs earlier than the onset of the perturbative regime as
measured by the start of the quasinormal ringing in the
gravitational waveforms, indicating that previous semianalytical
evidence on the early validity of perturbative methods during
a black hole merger is indeed correct.
The scalar quasinormal frequencies are also used to associate
a mass and a spin with each hypersurface: this measure is,
within our error bars, compatible with the horizon mass and spin
computed from the dynamical horizon framework.
The emerging physical picture indicates that the behavior of
a scalar field propagating on the spacetime of two merged
(i.e., surrounded by a common apparent horizon) black holes
is very close to that expected on a Kerr spacetime
with mass and spin parameters equal to the
mass and spin of the common apparent horizon at the end of
the coalescence.
Advisors/Committee Members: Deirdre Shoemaker, Committee Chair/Co-Chair, Pablo Laguna, Committee Member, Lee S Finn, Committee Member, Yousry Azmy, Committee Member.
Subjects/Keywords: Numerical relativity; black holes
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APA (6th Edition):
Bentivegna, E. (2008). Ringing in unison: exploring black hole coalescence with quasinormal modes. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/8245
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Bentivegna, Eloisa. “Ringing in unison: exploring black hole coalescence with quasinormal modes.” 2008. Thesis, Penn State University. Accessed March 01, 2021.
https://submit-etda.libraries.psu.edu/catalog/8245.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Bentivegna, Eloisa. “Ringing in unison: exploring black hole coalescence with quasinormal modes.” 2008. Web. 01 Mar 2021.
Vancouver:
Bentivegna E. Ringing in unison: exploring black hole coalescence with quasinormal modes. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Mar 01].
Available from: https://submit-etda.libraries.psu.edu/catalog/8245.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bentivegna E. Ringing in unison: exploring black hole coalescence with quasinormal modes. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/8245
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Otago
26.
Georgios, Doulis.
The Generalised Conformal Field Equations Near Spatial Infinity
.
Degree: 2013, University of Otago
URL: http://hdl.handle.net/10523/4088
The linearised general conformal field equations in their first and second order form are used to study the behaviour of the spin-2 zero-rest-mass equation on Minkowski background in the vicinity of space-like infinity.
Advisors/Committee Members: Frauendiener, Joerg (advisor).Subjects/Keywords: numerical relativity;
SBP operators;
SAT method;
conformal representation;
spatial infinity
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APA ·
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Manager
APA (6th Edition):
Georgios, D. (2013). The Generalised Conformal Field Equations Near Spatial Infinity
. (Doctoral Dissertation). University of Otago. Retrieved from http://hdl.handle.net/10523/4088
Chicago Manual of Style (16th Edition):
Georgios, Doulis. “The Generalised Conformal Field Equations Near Spatial Infinity
.” 2013. Doctoral Dissertation, University of Otago. Accessed March 01, 2021.
http://hdl.handle.net/10523/4088.
MLA Handbook (7th Edition):
Georgios, Doulis. “The Generalised Conformal Field Equations Near Spatial Infinity
.” 2013. Web. 01 Mar 2021.
Vancouver:
Georgios D. The Generalised Conformal Field Equations Near Spatial Infinity
. [Internet] [Doctoral dissertation]. University of Otago; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10523/4088.
Council of Science Editors:
Georgios D. The Generalised Conformal Field Equations Near Spatial Infinity
. [Doctoral Dissertation]. University of Otago; 2013. Available from: http://hdl.handle.net/10523/4088
University of Tasmania
27.
Inglis, SM.
The manifestly gauge invariant Maxwell-Dirac equations.
Degree: 2015, University of Tasmania
URL: https://eprints.utas.edu.au/23211/1/Inglis_whole_thesis.pdf
► We study the Maxwell-Dirac equations, which model the fermionic relativistic electrodynamics in the case where the fermion field is itself the source of the electromagnetic…
(more)
▼ We study the Maxwell-Dirac equations, which model the fermionic relativistic electrodynamics in the case where the fermion field is itself the source of the electromagnetic field. This system is formulated by exploiting that fact that the Dirac equation can be algebraically inverted, and the resulting expression for the vector potential in terms of the spinor fields can be directly substituted into Maxwell's equations.
We work in a formalism where the physical states are described by a set of tensor fields, formed from bilinear combinations of (non-Grassmann) spinor fields and Dirac matrices. This results in a set of manifestly gauge invariant equations that lack such unphysical degrees of freedom. Through the use of Fierz expansions on quadratic spinor combinations, and their associated identities, a large set of interrelationships between bilinear fields can be obtained. This permits the description of the Maxwell-Dirac system in terms of tensor current densities, and their quadratic Fierz identities and continuity constraints.
The resulting set of self-coupled Maxwell-Dirac equations is mathematically intractable without further constraint. We show how demanding invariance of the bilinear tensor fields under the action of arbitrary subgroups of the Poincarè group of rotations, translations and boosts reduces the equations to the point where they are more manageable. In this thesis, we demonstrate in detail how the Maxwell-Dirac equations reduce under several example subgroups.
We also develop the gauge invariant bilinear formalism for the stress-energy tensor, which can be used to calculate physical quantities such as the momentum and mass-energy corresponding to a Maxwell-Dirac solution. The calculation is approached from two independent points of view, namely the Belinfante method and the variational method from general relativity, which we find to be in agreement.
Finally, by analogy with the method in electromagnetism, we extend the algebraic inversion of the Dirac equation to the case where the spinors are isospin doublets, and the gauge field corresponds to the non-Abelian group SU(2). Following the definition of non-Abelian bilinears and Fierz identities, the inverted form itself is given formally, with the application of a Neumann series required for an explicit expression.
Subjects/Keywords: Electromagnetism; Relativity; Quantum Mechanics; Differential Equations; Symmetry Groups; Numerical Solutions
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APA (6th Edition):
Inglis, S. (2015). The manifestly gauge invariant Maxwell-Dirac equations. (Thesis). University of Tasmania. Retrieved from https://eprints.utas.edu.au/23211/1/Inglis_whole_thesis.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Inglis, SM. “The manifestly gauge invariant Maxwell-Dirac equations.” 2015. Thesis, University of Tasmania. Accessed March 01, 2021.
https://eprints.utas.edu.au/23211/1/Inglis_whole_thesis.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Inglis, SM. “The manifestly gauge invariant Maxwell-Dirac equations.” 2015. Web. 01 Mar 2021.
Vancouver:
Inglis S. The manifestly gauge invariant Maxwell-Dirac equations. [Internet] [Thesis]. University of Tasmania; 2015. [cited 2021 Mar 01].
Available from: https://eprints.utas.edu.au/23211/1/Inglis_whole_thesis.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Inglis S. The manifestly gauge invariant Maxwell-Dirac equations. [Thesis]. University of Tasmania; 2015. Available from: https://eprints.utas.edu.au/23211/1/Inglis_whole_thesis.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Syracuse University
28.
Pekowsky, Larne.
Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences.
Degree: PhD, Physics, 2011, Syracuse University
URL: https://surface.syr.edu/phy_etd/116
► Gravitational waves are a consequence of the general theory of relativity. Direct detection of such waves will provide a wealth of information about physics,…
(more)
▼ Gravitational waves are a consequence of the general theory of
relativity. Direct detection of such waves will provide a wealth of information about physics, astronomy, and cosmology. A worldwide effort is currently underway to make the first direct detection of gravitational waves. The global network of detectors includes the Laser Interferometer Gravitational-wave Observatory (LIGO), which recently completed its sixth science run.
A particularly promising source of gravitational waves is a binary system consisting of two neutron stars and/or black holes. As the objects orbit each other they emit gravitational radiation, lose energy, and spiral inwards. This produces a characteristic ``chirp'' signal for which we can search in the LIGO data. Currently this is done using matched-filter techniques, which correlate the detector data against analytic models of the emitted gravitational waves. Several choices must be made in constructing a search for signals from such binary coalescences.
Any discrepancy between the signals and the models used will reduce the effectiveness of the matched filter. However, the analytic models are based on approximations which are not valid through the entire evolution of the binary. In recent years
numerical relativity has had impressive success in simulating the final phases of the coalescence of binary black holes. While
numerical relativity is too computationally expensive to use directly in the search, this progress has made it possible to perform realistic tests of the LIGO searches. The results of such tests can be used to improve the efficiency of searches.
Conversely, noise in the LIGO and Virgo detectors can reduce the efficiency. This must be addressed by characterizing the quality of the data from the detectors, and removing from the analysis times that will be detrimental to the search.
In this thesis we utilize recent results from
numerical relativity to study both the degree to which analytic models match realistic waveforms and the ability of LIGO searches to make detections. We also apply the matched-filter search to the problem of removing times of excess noise from the search.
Advisors/Committee Members: Duncan Brown.
Subjects/Keywords: Black holes; Gravitational waves; LIGO; Numerical relativity; Physics
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APA ·
Chicago ·
MLA ·
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APA (6th Edition):
Pekowsky, L. (2011). Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences. (Doctoral Dissertation). Syracuse University. Retrieved from https://surface.syr.edu/phy_etd/116
Chicago Manual of Style (16th Edition):
Pekowsky, Larne. “Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences.” 2011. Doctoral Dissertation, Syracuse University. Accessed March 01, 2021.
https://surface.syr.edu/phy_etd/116.
MLA Handbook (7th Edition):
Pekowsky, Larne. “Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences.” 2011. Web. 01 Mar 2021.
Vancouver:
Pekowsky L. Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences. [Internet] [Doctoral dissertation]. Syracuse University; 2011. [cited 2021 Mar 01].
Available from: https://surface.syr.edu/phy_etd/116.
Council of Science Editors:
Pekowsky L. Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences. [Doctoral Dissertation]. Syracuse University; 2011. Available from: https://surface.syr.edu/phy_etd/116
University of Cambridge
29.
Liu, Rex Gerry.
Discrete gravitational approaches to cosmology.
Degree: PhD, 2015, University of Cambridge
URL: https://doi.org/10.17863/CAM.16141
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253
► Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable…
(more)
▼ Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable example is the FLRW metric underlying modern cosmology: the universe is assumed to be perfectly homogeneous and isotropic, but in the late universe, this is only true on average and only at large scales. Where an exact solution is not available, discrete gravitational approaches can approximate the system instead. This thesis investigates several cosmological systems using two distinct discrete approaches. Closed, flat, and open ‘lattice universes’ are first considered where matter is distributed as a regular lattice of identical point masses in constant-time hypersurfaces. Lindquist and Wheeler’s Schwarzschild–cell method is applied where the lattice cell around each mass is approximated by a perfectly spherical cell with Schwarzschild space–time inside. The resulting dynamics and cosmological redshifts closely resemble those of the dust-filled FLRW universes, but with certain differences in redshift behaviour attributable to the lattice universe’s lumpiness. The application of Regge calculus to cosmology is considered next. We focus exclusively on the closed models developed by Collins, Williams, and Brewin. Their approach is first applied to a universe where an exact solution is already well-established, the vacuum Λ-FLRW model. The resulting models are found to closely reproduce the dynamics of the continuum model being approximated, though certain constraints on the applicability of the approach are also uncovered. Then using this knowledge, we next model the closed lattice universe. The resulting evolution closely resembles that of the closed dust-filled FLRW universe. Constraints on the placement of the masses in the Regge skeleton are also uncovered. Finally, a ‘lattice universe’ with one perturbed mass is modelled. The evolution is still stable and similar to that of the unperturbed model. The thesis concludes by discussing possible extensions of our work.
Subjects/Keywords: 523.1; cosmology; general relativity; gravitation; discrete gravity; numerical gravity; Regge calculus
Record Details
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Record Details
Similar Records
Cite
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Liu, R. G. (2015). Discrete gravitational approaches to cosmology. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.16141 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253
Chicago Manual of Style (16th Edition):
Liu, Rex Gerry. “Discrete gravitational approaches to cosmology.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.16141 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253.
MLA Handbook (7th Edition):
Liu, Rex Gerry. “Discrete gravitational approaches to cosmology.” 2015. Web. 01 Mar 2021.
Vancouver:
Liu RG. Discrete gravitational approaches to cosmology. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.16141 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253.
Council of Science Editors:
Liu RG. Discrete gravitational approaches to cosmology. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://doi.org/10.17863/CAM.16141 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253
30.
Liu, Rex Gerry.
Discrete gravitational approaches to cosmology.
Degree: PhD, 2015, University of Cambridge
URL: https://www.repository.cam.ac.uk/handle/1810/249027https://www.repository.cam.ac.uk/bitstream/1810/249027/3/LW%20C%2b%2b%20code.zip
;
https://www.repository.cam.ac.uk/bitstream/1810/249027/4/license_rdf
;
https://www.repository.cam.ac.uk/bitstream/1810/249027/2/license.txt
;
https://www.repository.cam.ac.uk/bitstream/1810/249027/8/RGLiu%20-%20thesis%20-%20updated.pdf.txt
;
https://www.repository.cam.ac.uk/bitstream/1810/249027/9/RGLiu%20-%20thesis%20-%20updated.pdf.jpg
► Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable…
(more)
▼ Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable example is the FLRW metric underlying modern cosmology: the universe is assumed to be perfectly homogeneous and isotropic, but in the late universe, this is only true on average and only at large scales. Where an exact solution is not available, discrete gravitational approaches can approximate the system instead. This thesis investigates several cosmological systems using two distinct discrete approaches. Closed, flat, and open ‘lattice universes’ are first considered where matter is distributed as a regular lattice of identical point masses in constant-time hypersurfaces. Lindquist and Wheeler’s Schwarzschild–cell method is applied where the lattice cell around each mass is approximated by a perfectly spherical cell with Schwarzschild space–time inside. The resulting dynamics and cosmological redshifts closely resemble those of the dust-filled FLRW universes, but with certain differences in redshift behaviour attributable to the lattice universe’s lumpiness. The application of Regge calculus to cosmology is considered next. We focus exclusively on the closed models developed by Collins, Williams, and Brewin. Their approach is first applied to a universe where an exact solution is already well-established, the vacuum Λ-FLRW model. The resulting models are found to closely reproduce the dynamics of the continuum model being approximated, though certain constraints on the applicability of the approach are also uncovered. Then using this knowledge, we next model the closed lattice universe. The resulting evolution closely resembles that of the closed dust-filled FLRW universe. Constraints on the placement of the masses in the Regge skeleton are also uncovered. Finally, a ‘lattice universe’ with one perturbed mass is modelled. The evolution is still stable and similar to that of the unperturbed model. The thesis concludes by discussing possible extensions of our work.
Subjects/Keywords: cosmology; general relativity; gravitation; discrete gravity; numerical gravity; Regge calculus
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Liu, R. G. (2015). Discrete gravitational approaches to cosmology. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/249027https://www.repository.cam.ac.uk/bitstream/1810/249027/3/LW%20C%2b%2b%20code.zip ; https://www.repository.cam.ac.uk/bitstream/1810/249027/4/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/249027/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/8/RGLiu%20-%20thesis%20-%20updated.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/9/RGLiu%20-%20thesis%20-%20updated.pdf.jpg
Chicago Manual of Style (16th Edition):
Liu, Rex Gerry. “Discrete gravitational approaches to cosmology.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://www.repository.cam.ac.uk/handle/1810/249027https://www.repository.cam.ac.uk/bitstream/1810/249027/3/LW%20C%2b%2b%20code.zip ; https://www.repository.cam.ac.uk/bitstream/1810/249027/4/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/249027/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/8/RGLiu%20-%20thesis%20-%20updated.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/9/RGLiu%20-%20thesis%20-%20updated.pdf.jpg.
MLA Handbook (7th Edition):
Liu, Rex Gerry. “Discrete gravitational approaches to cosmology.” 2015. Web. 01 Mar 2021.
Vancouver:
Liu RG. Discrete gravitational approaches to cosmology. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 01].
Available from: https://www.repository.cam.ac.uk/handle/1810/249027https://www.repository.cam.ac.uk/bitstream/1810/249027/3/LW%20C%2b%2b%20code.zip ; https://www.repository.cam.ac.uk/bitstream/1810/249027/4/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/249027/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/8/RGLiu%20-%20thesis%20-%20updated.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/9/RGLiu%20-%20thesis%20-%20updated.pdf.jpg.
Council of Science Editors:
Liu RG. Discrete gravitational approaches to cosmology. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://www.repository.cam.ac.uk/handle/1810/249027https://www.repository.cam.ac.uk/bitstream/1810/249027/3/LW%20C%2b%2b%20code.zip ; https://www.repository.cam.ac.uk/bitstream/1810/249027/4/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/249027/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/8/RGLiu%20-%20thesis%20-%20updated.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/249027/9/RGLiu%20-%20thesis%20-%20updated.pdf.jpg
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Open Access Theses and Dissertations
