subject:(Numerical Relativity)

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 (6^th 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 (16^th Edition):

Field, Scott Edward. “Applications of Discontinuous Galerkin Methods to Computational General Relativity.” 2011. Doctoral Dissertation, Brown University. Accessed July 24, 2019. https://repository.library.brown.edu/studio/item/bdr:11327/.

MLA Handbook (7^th Edition):

Field, Scott Edward. “Applications of Discontinuous Galerkin Methods to Computational General Relativity.” 2011. Web. 24 Jul 2019.

Vancouver:

Field SE. Applications of Discontinuous Galerkin Methods to Computational General Relativity. [Internet] [Doctoral dissertation]. Brown University; 2011. [cited 2019 Jul 24]. 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/

Penn State University

2. Bentivegna, Eloisa. Ringing in unison: exploring black hole coalescence with quasinormal modes.

Degree: PhD, Physics, 2008, Penn State University

URL: https://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)

Subjects/Keywords: Numerical relativity; black holes

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APA (6^th Edition):

Bentivegna, E. (2008). Ringing in unison: exploring black hole coalescence with quasinormal modes. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/8245

Chicago Manual of Style (16^th Edition):

Bentivegna, Eloisa. “Ringing in unison: exploring black hole coalescence with quasinormal modes.” 2008. Doctoral Dissertation, Penn State University. Accessed July 24, 2019. https://etda.libraries.psu.edu/catalog/8245.

MLA Handbook (7^th Edition):

Bentivegna, Eloisa. “Ringing in unison: exploring black hole coalescence with quasinormal modes.” 2008. Web. 24 Jul 2019.

Vancouver:

Bentivegna E. Ringing in unison: exploring black hole coalescence with quasinormal modes. [Internet] [Doctoral dissertation]. Penn State University; 2008. [cited 2019 Jul 24]. Available from: https://etda.libraries.psu.edu/catalog/8245.

Council of Science Editors:

Bentivegna E. Ringing in unison: exploring black hole coalescence with quasinormal modes. [Doctoral Dissertation]. Penn State University; 2008. Available from: https://etda.libraries.psu.edu/catalog/8245

Louisiana State University

3. 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)

Subjects/Keywords: numerical relativity

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APA (6^th 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 (16^th Edition):

Calabrese, Gioel. “Constraint preserving boundary conditions for the linearized Einstein equations.” 2003. Doctoral Dissertation, Louisiana State University. Accessed July 24, 2019. etd-1105103-100340 ; https://digitalcommons.lsu.edu/gradschool_dissertations/346.

MLA Handbook (7^th Edition):

Calabrese, Gioel. “Constraint preserving boundary conditions for the linearized Einstein equations.” 2003. Web. 24 Jul 2019.

Vancouver:

Calabrese G. Constraint preserving boundary conditions for the linearized Einstein equations. [Internet] [Doctoral dissertation]. Louisiana State University; 2003. [cited 2019 Jul 24]. 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

Rochester Institute of Technology

4. 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)

Subjects/Keywords: Applied mathematics; Math; Numerical relativity

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APA (6^th 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 (16^th Edition):

Rosato, Nicole. “Visualization and Analysis of a Numerical Simulation of GW150914.” 2017. Masters Thesis, Rochester Institute of Technology. Accessed July 24, 2019. https://scholarworks.rit.edu/theses/9609.

MLA Handbook (7^th Edition):

Rosato, Nicole. “Visualization and Analysis of a Numerical Simulation of GW150914.” 2017. Web. 24 Jul 2019.

Vancouver:

Rosato N. Visualization and Analysis of a Numerical Simulation of GW150914. [Internet] [Masters thesis]. Rochester Institute of Technology; 2017. [cited 2019 Jul 24]. 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

Penn State University

5. Wood, Shaun Patrick. Curvature Scalar Diagnostics and Progress on a Chern-Simons Initial Value Formulation.

Degree: PhD, Physics, 2009, Penn State University

URL: https://etda.libraries.psu.edu/catalog/10148

► In the recent past, many numerical relativity groups have gained the ability to perform fully relativistic simulations of black hole mergers. One of the key… (more)

▼ In the recent past, many numerical relativity groups have gained the ability to perform fully relativistic simulations of black hole mergers. One of the key aims of these simulations is to compute gravitational waveforms. Such waveforms are interesting not only from a theoretical standpoint, but also because they are necessary for the ongoing effort to detect gravitational waves. Current numerical methods for computing gravitational waveforms depend on assumptions made about the background spacetime, typically via a choice of tetrad. Such methods require additional checks to insure the assumptions are correct. In this dissertation, we first present the results of a project to use scalars which can be computed using only contractions of the curvature tensor as diagnostic tools in numerical relativity simulations. The scalars have been shown to contain information about the background spacetime and gravitational radiation, and are independent of any choice of tetrad, background, or coordinates. The Baker Campanelli speciality index is used to determine when the spacetime separates into background and radiation, subject to the conditions that the radiation be weak and be purely outgoing. We find that at least the second condition is not satisfied in the simulations we perform. Then, the Beetle-Burko radiation scalar is used to check the assumption that the tetrad used to compute gravitational waveforms represents the principle null directions of the background spacetime. It is essential that two vectors of the tetrad are parallel to the two principle null directions of the background in order to interpret the Newman Penrose scalar Ψ₄ as the outgoing gravitational wave. We find the tetrad passes this test whenever it can be applied in our simulations. While this does not permit us to conclude that the scalar Ψ₄ is the outgoing gravitational wave, the test can be used in more generic simulations to catch errors in the Ψ₄ calculation. Next, we present an attempt to write Chern-Simons modified gravity as an initial value problem. Chern-Simons modified gravity is an extension to general relativity in which a parity violating term is added to the action. One effect the modification has is to enhance or suppress the different polarizations of gravitational radiation. Therefore, there is great interest in simulating binary black hole mergers in the theory and computing the resulting gravitational radiation. We provide an incomplete set of constraints and evolution equations for the theory, and discuss difficulties of finding a complete set. Projections of the modified field equations are also provided. Once a complete initial value formulation is found and simulations are performed, gravitational wave detection can provide a strong test of Chern-Simons modified gravity.

Subjects/Keywords: general relativity; numerical relativity; Beetle-Burko scalar; Chern-Simons gravity

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APA (6^th Edition):

Wood, S. P. (2009). Curvature Scalar Diagnostics and Progress on a Chern-Simons Initial Value Formulation. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/10148

Chicago Manual of Style (16^th Edition):

Wood, Shaun Patrick. “Curvature Scalar Diagnostics and Progress on a Chern-Simons Initial Value Formulation.” 2009. Doctoral Dissertation, Penn State University. Accessed July 24, 2019. https://etda.libraries.psu.edu/catalog/10148.

MLA Handbook (7^th Edition):

Wood, Shaun Patrick. “Curvature Scalar Diagnostics and Progress on a Chern-Simons Initial Value Formulation.” 2009. Web. 24 Jul 2019.

Vancouver:

Wood SP. Curvature Scalar Diagnostics and Progress on a Chern-Simons Initial Value Formulation. [Internet] [Doctoral dissertation]. Penn State University; 2009. [cited 2019 Jul 24]. Available from: https://etda.libraries.psu.edu/catalog/10148.

Council of Science Editors:

Wood SP. Curvature Scalar Diagnostics and Progress on a Chern-Simons Initial Value Formulation. [Doctoral Dissertation]. Penn State University; 2009. Available from: https://etda.libraries.psu.edu/catalog/10148

University of Cambridge

6. Cook, William. Numerical relativity in higher dimensional spacetimes.

Degree: PhD, 2018, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/277718 ; http://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: General Relativity; Numerical Relativity; Black Holes; Higher Dimensions

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APA (6^th Edition):

Cook, W. (2018). Numerical relativity in higher dimensional spacetimes. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/277718 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999

Chicago Manual of Style (16^th Edition):

Cook, William. “Numerical relativity in higher dimensional spacetimes.” 2018. Doctoral Dissertation, University of Cambridge. Accessed July 24, 2019. https://www.repository.cam.ac.uk/handle/1810/277718 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999.

MLA Handbook (7^th Edition):

Cook, William. “Numerical relativity in higher dimensional spacetimes.” 2018. Web. 24 Jul 2019.

Vancouver:

Cook W. Numerical relativity in higher dimensional spacetimes. [Internet] [Doctoral dissertation]. University of Cambridge; 2018. [cited 2019 Jul 24]. Available from: https://www.repository.cam.ac.uk/handle/1810/277718 ; http://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://www.repository.cam.ac.uk/handle/1810/277718 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.744999

7. 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, Mihail Barbosu, Manuela Campanelli.

Subjects/Keywords: Black hole; Evolution; General relativity; Initial data; Numerical relativity; Spin

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APA (6^th 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 (16^th 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 July 24, 2019. https://scholarworks.rit.edu/theses/8797.

MLA Handbook (7^th Edition):

Ruchlin, Ian. “Puncture Initial Data and Evolution of Black Hole Binaries with High Speed and High Spin.” 2015. Web. 24 Jul 2019.

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 2019 Jul 24]. 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

Georgia Tech

8. 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)

Subjects/Keywords: Numerical relativity; Astrophysics; Neutron stars; Gravitational waves

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APA (6^th 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 (16^th Edition):

Clark, Michael C. “Bowen-type initial data for simulations of neutron stars in binary systems.” 2016. Doctoral Dissertation, Georgia Tech. Accessed July 24, 2019. http://hdl.handle.net/1853/55005.

MLA Handbook (7^th Edition):

Clark, Michael C. “Bowen-type initial data for simulations of neutron stars in binary systems.” 2016. Web. 24 Jul 2019.

Vancouver:

Clark MC. Bowen-type initial data for simulations of neutron stars in binary systems. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2019 Jul 24]. 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

9. Hemberger, Daniel. Numerical Evolutions Of Binary Black Hole Systems .

Degree: 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…

5 more images…

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APA (6^th Edition):

Hemberger, D. (2013). Numerical Evolutions Of Binary Black Hole Systems . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/34160

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hemberger, Daniel. “Numerical Evolutions Of Binary Black Hole Systems .” 2013. Thesis, Cornell University. Accessed July 24, 2019. http://hdl.handle.net/1813/34160.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hemberger, Daniel. “Numerical Evolutions Of Binary Black Hole Systems .” 2013. Web. 24 Jul 2019.

Vancouver:

Hemberger D. Numerical Evolutions Of Binary Black Hole Systems . [Internet] [Thesis]. Cornell University; 2013. [cited 2019 Jul 24]. Available from: http://hdl.handle.net/1813/34160.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hemberger D. Numerical Evolutions Of Binary Black Hole Systems . [Thesis]. Cornell University; 2013. Available from: http://hdl.handle.net/1813/34160

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Rochester Institute of Technology

10. 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)

Subjects/Keywords: Binary black holes; Gravitational waves; Numerical relativity

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APA (6^th 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 (16^th 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 July 24, 2019. https://scholarworks.rit.edu/theses/9323.

MLA Handbook (7^th Edition):

Lange, Jacob A. “Directly comparing synthetic and real binary black hole coalescence sources with numerical solutions of Einstein’s equation.” 2016. Web. 24 Jul 2019.

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 2019 Jul 24]. 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

Leiden University

11. 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)

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 (6^th 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 (16^th Edition):

Sterk, Peter. “Formation of black branes with U(1) scalar hair.” 2017. Masters Thesis, Leiden University. Accessed July 24, 2019. http://hdl.handle.net/1887/52788.

MLA Handbook (7^th Edition):

Sterk, Peter. “Formation of black branes with U(1) scalar hair.” 2017. Web. 24 Jul 2019.

Vancouver:

Sterk P. Formation of black branes with U(1) scalar hair. [Internet] [Masters thesis]. Leiden University; 2017. [cited 2019 Jul 24]. 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

Georgia Tech

12. 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)

Subjects/Keywords: Numerical Relativity; Hydrodynamics; General Relativity; Smoothed Particle Hydrodynamics; Hierarchical Spatial Hashing; Parallel Computing

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APA (6^th 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 (16^th 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 July 24, 2019. http://hdl.handle.net/1853/55557.

MLA Handbook (7^th Edition):

Kinsey, Matthew Christopher. “General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity.” 2016. Web. 24 Jul 2019.

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 2019 Jul 24]. 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 Cambridge

13. Kunesch, Markus. Numerical simulations of instabilities in general relativity.

Degree: PhD, 2018, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/283135 ; 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: general relativity; black holes; cosmic censorship; numerical relativity; higher dimensions; AdS; adaptive mesh refinement

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APA (6^th Edition):

Kunesch, M. (2018). Numerical simulations of instabilities in general relativity. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/283135 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593

Chicago Manual of Style (16^th Edition):

Kunesch, Markus. “Numerical simulations of instabilities in general relativity.” 2018. Doctoral Dissertation, University of Cambridge. Accessed July 24, 2019. https://www.repository.cam.ac.uk/handle/1810/283135 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593.

MLA Handbook (7^th Edition):

Kunesch, Markus. “Numerical simulations of instabilities in general relativity.” 2018. Web. 24 Jul 2019.

Vancouver:

Kunesch M. Numerical simulations of instabilities in general relativity. [Internet] [Doctoral dissertation]. University of Cambridge; 2018. [cited 2019 Jul 24]. Available from: https://www.repository.cam.ac.uk/handle/1810/283135 ; 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://www.repository.cam.ac.uk/handle/1810/283135 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.763593

Syracuse University

14. 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 · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th 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 (16^th 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 July 24, 2019. https://surface.syr.edu/phy_etd/116.

MLA Handbook (7^th Edition):

Pekowsky, Larne. “Characterization of Enhanced Interferometric Gravitational Wave Detectors and Studies of Numeric Simulations for Compact-Binary Coalescences.” 2011. Web. 24 Jul 2019.

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 2019 Jul 24]. 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

Penn State University

15. Healy, James. The Final State from Generic Binary Black Hole Coalescence: Mass, Spin, and Gravitational Recoil.

Degree: PhD, Physics, 2009, Penn State University

URL: https://etda.libraries.psu.edu/catalog/10259

► Since the breakthroughs of numerically solving Einstein's Equations of gravity in the early 21st century, numerical relativity has been used primarily to study the most… (more)

▼ Since the breakthroughs of numerically solving Einstein's Equations of gravity in the early 21st century, numerical relativity has been used primarily to study the most astrophysically relevant binary black hole configuration, the quasi-circular inspiral. Various aspects of the quasi-circular system with different spin configurations have been studied, including the gravitational radiation and the final state of the spacetime, that is, its mass, spin, and recoil velocity (or kick). However, these quasi-circular configurations cover a small sliver of the parameter space of solutions for binary black hole spacetimes. This dissertation explores the final state from generic binary black hole coalescence, considering a broad range of initial orbital configurations, from direct plunges to escape and recapture events to quasi-circular inspirals and to even more energetic orbits. Gravitational recoil is caused by the anisotropic emission of gravitational radiation due to asymmetries in the initial binary black hole spacetime. For quasi-circular inspirals, the beamed radiation tends to average over the inspiral, with the main contribution coming from the plunge. By considering hyperbolic encounters that are plunge-dominated, we observe an enhancement of the preferential beaming leading to kick velocities of ~ 10,000 km/s for the sequence studied, about 2.5X larger than the highest projected kick from a quasi-circular configuration. Despite the higher magnitude kicks produced, these systems exhibit the same general dependence of the kick on the initial spin configurations as the quasi-circular system. The final spin of the system is determined by the residual orbital and spin angular momentum that is not radiated in the process of merging. Considering plunge-dominated systems with a broad range of initial spin configurations and impact angles provides a comprehensive search of those configurations that maximize the final spin of the remnant black hole. We estimate that the final spin can reach a maximum a/M_h ~ 0.992 for extremal spinning, equal-mass black hole mergers. In addition, we find that as one increases the orbital angular momentum, the mergers produce black holes with mass and spin oscillating around the values of a golden black hole. We find that the values of the parameters for the golden black hole correspond to the final state of the black hole obtained from the quasi-circular system with the same spin configuration. Lastly, we confirm that zoom-whirl behavior can survive the dissipatory drain of full General Relativity and is not confined to a finely tuned region of initial parameters.

Subjects/Keywords: Black Hole; Binary Black Holes; Numerical Relativity; Gravitational Waves; Final State

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Healy, J. (2009). The Final State from Generic Binary Black Hole Coalescence: Mass, Spin, and Gravitational Recoil. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/10259

Chicago Manual of Style (16^th Edition):

Healy, James. “The Final State from Generic Binary Black Hole Coalescence: Mass, Spin, and Gravitational Recoil.” 2009. Doctoral Dissertation, Penn State University. Accessed July 24, 2019. https://etda.libraries.psu.edu/catalog/10259.

MLA Handbook (7^th Edition):

Healy, James. “The Final State from Generic Binary Black Hole Coalescence: Mass, Spin, and Gravitational Recoil.” 2009. Web. 24 Jul 2019.

Vancouver:

Healy J. The Final State from Generic Binary Black Hole Coalescence: Mass, Spin, and Gravitational Recoil. [Internet] [Doctoral dissertation]. Penn State University; 2009. [cited 2019 Jul 24]. Available from: https://etda.libraries.psu.edu/catalog/10259.

Council of Science Editors:

Healy J. The Final State from Generic Binary Black Hole Coalescence: Mass, Spin, and Gravitational Recoil. [Doctoral Dissertation]. Penn State University; 2009. Available from: https://etda.libraries.psu.edu/catalog/10259

Cornell University

16. Foucart, Francois. Numerical Studies Of Black Hole-Neutron Star Binaries .

Degree: 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)

Subjects/Keywords: General Relativity; Black Hole-Neutron Star Binaries; Numerical Simulations

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APA (6^th Edition):

Foucart, F. (2011). Numerical Studies Of Black Hole-Neutron Star Binaries . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/30652

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Foucart, Francois. “Numerical Studies Of Black Hole-Neutron Star Binaries .” 2011. Thesis, Cornell University. Accessed July 24, 2019. http://hdl.handle.net/1813/30652.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Foucart, Francois. “Numerical Studies Of Black Hole-Neutron Star Binaries .” 2011. Web. 24 Jul 2019.

Vancouver:

Foucart F. Numerical Studies Of Black Hole-Neutron Star Binaries . [Internet] [Thesis]. Cornell University; 2011. [cited 2019 Jul 24]. Available from: http://hdl.handle.net/1813/30652.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Foucart F. Numerical Studies Of Black Hole-Neutron Star Binaries . [Thesis]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/30652

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Otago

17. 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 (6^th 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 (16^th Edition):

Georgios, Doulis. “The Generalised Conformal Field Equations Near Spatial Infinity .” 2013. Doctoral Dissertation, University of Otago. Accessed July 24, 2019. http://hdl.handle.net/10523/4088.

MLA Handbook (7^th Edition):

Georgios, Doulis. “The Generalised Conformal Field Equations Near Spatial Infinity .” 2013. Web. 24 Jul 2019.

Vancouver:

Georgios D. The Generalised Conformal Field Equations Near Spatial Infinity . [Internet] [Doctoral dissertation]. University of Otago; 2013. [cited 2019 Jul 24]. 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

18. 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 (6^th 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 (16^th Edition):

Inglis, SM. “The manifestly gauge invariant Maxwell-Dirac equations.” 2015. Thesis, University of Tasmania. Accessed July 24, 2019. 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 (7^th Edition):

Inglis, SM. “The manifestly gauge invariant Maxwell-Dirac equations.” 2015. Web. 24 Jul 2019.

Vancouver:

Inglis S. The manifestly gauge invariant Maxwell-Dirac equations. [Internet] [Thesis]. University of Tasmania; 2015. [cited 2019 Jul 24]. 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

Universitat de Valencia

19. Mewes, Vassilios. Numerical relativity simulations of tilted black hole-torus systems .

Degree: 2016, Universitat de Valencia

URL: http://hdl.handle.net/10550/54494

► Las fusiones de objetos compactos se encuentran entre los eventos más interesantes de la astrofísica relativista, siendo, en particular, el principal objetivo de la astronomía… (more)

▼ Las fusiones de objetos compactos se encuentran entre los eventos más interesantes de la astrofísica relativista, siendo, en particular, el principal objetivo de la astronomía de ondas gravitatorias. En esta tesis investigamos los posibles estados finales de la fusión de sistemas binarios formados por agujero negro-estrella de neutrones o por dos estrellas de neutrones: discos gruesos (o toros) de acrecimiento alrededor de agujeros negros en rotación tipo Kerr. Estos sistemas agujero negro-toro se cree que constituyen el motor central de los eventos más luminosos del Universo: los llamados estallidos de rayos gamma. Nuestro conocimiento sobre la evolución y la estabilidad de estos sistemas depende crucialmente de la realización de simulaciones numéricas precisas de su dinámica, en el contexto de la relatividad numérica, es decir, tanto el espacio-tiempo como la materia. El principal trabajo de esta tesis es llevar a cabo tales simulaciones en relatividad numérica de sistemas agujero negro-toro. Para ello utilizamos modelos de equilibrio de discos auto-gravitantes alrededor de agujeros negros como datos iniciales, los cuales representan modelos idealizados (aunque apropiados) de los discos post-fusión reales obtenidos de manera auto-consistente en simulaciones de fusión de binarias compactas en relatividad numérica. Tradicionalmente, la simulación numérica de estos sistemas se ha realizado bajo la hipótesis de que el espín del agujero negro y el momento angular del disco están alineados. Sin embargo, existen razones para creer que muchos de estos sistemas deberían estar inclinados, lo cual significa que el plano ecuatorial del disco ya no es paralelo al del agujero negro. Ciertamente, sistemas agujero negro-toro inclinados se han obtenido auto-consistentemente en simulaciones de relatividad numérica de la fusión de un agujero negro y una estrella de neutrones con los momentos angulares no alineados. En tales sistemas inclinados, la dinámica del sistema agujero negro-toro cambia completamente con respecto al caso alineado, debido a los efectos de relatividad general que surgen de la estructura del espacio tiempo de la métrica de Kerr. Especialmente, debido a la precesión diferencial de Lense-Thirring, el disco puede l legar a estar trenzado y combado. Para capturar la respuesta dinámica correcta de estos efectos en la evolución del disco es necesario evolucionar los sistemas mediante simulaciones hidrodinámicas en relatividad general. El trabajo pionero en este campo fue llevado a cabo por Fragile y colaboradores, quienes realizaron las primeras simulaciones relativistas de sistemas agujero negro-toro inclinados en la aproximación fluido de prueba, es decir, asumiendo que el espacio-tiempo se mantiene inalterado en el tiempo e ignorando la auto-gravedad del disco. Basándonos en este influyente trabajo, hemos realizado en esta tesis el primer estudio numérico sistemático de sistemas agujero negro-toro inclinados en un espacio-tiempo totalmente evolucionado. … Advisors/Committee Members: Font Roda, José Antonio (advisor).

Subjects/Keywords: accretion, accretion discs; black hole physics; hydrodynamics; instabilities; numerical relativity

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APA (6^th Edition):

Mewes, V. (2016). Numerical relativity simulations of tilted black hole-torus systems . (Doctoral Dissertation). Universitat de Valencia. Retrieved from http://hdl.handle.net/10550/54494

Chicago Manual of Style (16^th Edition):

Mewes, Vassilios. “Numerical relativity simulations of tilted black hole-torus systems .” 2016. Doctoral Dissertation, Universitat de Valencia. Accessed July 24, 2019. http://hdl.handle.net/10550/54494.

MLA Handbook (7^th Edition):

Mewes, Vassilios. “Numerical relativity simulations of tilted black hole-torus systems .” 2016. Web. 24 Jul 2019.

Vancouver:

Mewes V. Numerical relativity simulations of tilted black hole-torus systems . [Internet] [Doctoral dissertation]. Universitat de Valencia; 2016. [cited 2019 Jul 24]. Available from: http://hdl.handle.net/10550/54494.

Council of Science Editors:

Mewes V. Numerical relativity simulations of tilted black hole-torus systems . [Doctoral Dissertation]. Universitat de Valencia; 2016. Available from: http://hdl.handle.net/10550/54494

Cornell University

20. Henriksson, Katherine. Topics In Neutron Star Physics .

Degree: 2015, Cornell University

URL: http://hdl.handle.net/1813/39369

Subjects/Keywords: Neutron Stars; Superconductivity; Numerical Relativity

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Henriksson, K. (2015). Topics In Neutron Star Physics . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/39369

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Henriksson, Katherine. “Topics In Neutron Star Physics .” 2015. Thesis, Cornell University. Accessed July 24, 2019. http://hdl.handle.net/1813/39369.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Henriksson, Katherine. “Topics In Neutron Star Physics .” 2015. Web. 24 Jul 2019.

Vancouver:

Henriksson K. Topics In Neutron Star Physics . [Internet] [Thesis]. Cornell University; 2015. [cited 2019 Jul 24]. Available from: http://hdl.handle.net/1813/39369.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Henriksson K. Topics In Neutron Star Physics . [Thesis]. Cornell University; 2015. Available from: http://hdl.handle.net/1813/39369

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Cambridge

21. Liu, Rex Gerry. Discrete gravitational approaches to cosmology.

Degree: PhD, 2015, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/249027 ; 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

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APA (6^th Edition):

Liu, R. G. (2015). Discrete gravitational approaches to cosmology. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/249027 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253

Chicago Manual of Style (16^th Edition):

Liu, Rex Gerry. “Discrete gravitational approaches to cosmology.” 2015. Doctoral Dissertation, University of Cambridge. Accessed July 24, 2019. https://www.repository.cam.ac.uk/handle/1810/249027 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253.

MLA Handbook (7^th Edition):

Liu, Rex Gerry. “Discrete gravitational approaches to cosmology.” 2015. Web. 24 Jul 2019.

Vancouver:

Liu RG. Discrete gravitational approaches to cosmology. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2019 Jul 24]. Available from: https://www.repository.cam.ac.uk/handle/1810/249027 ; 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://www.repository.cam.ac.uk/handle/1810/249027 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.659253

Rochester Institute of Technology

22. 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 r⁴, where r is the spherical radius assuming the black hole is at the coordinate origin, making the Hamiltonian equation, which, unaltered, is a C² equation, become a C⁷ 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, Tony A. Harkin, Chris Wahle.

Subjects/Keywords: Black hole; Initial data; Numerical relativity; Pseudo spectral

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APA (6^th 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 (16^th 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 July 24, 2019. https://scholarworks.rit.edu/theses/9080.

MLA Handbook (7^th Edition):

Munro, Eugene. “Using Analytic Techniques to Resolve Numerical Issues in a Pseudo Spectral Solver for a Black Hole Scalar Field.” 2013. Web. 24 Jul 2019.

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 2019 Jul 24]. 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

23. 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)

Subjects/Keywords: Inverse curl; Magnetic heilcity; Magnetohydrodynamics; Numerical relativity; Vector potential

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APA (6^th 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 (16^th 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 July 24, 2019. https://scholarworks.rit.edu/theses/9878.

MLA Handbook (7^th Edition):

Silberman, Zachary J. “Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics.” 2018. Web. 24 Jul 2019.

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 2019 Jul 24]. 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

Penn State University

24. Smith, Kenneth Lee. Dynamic Singularity Excision in Numerical Relativity.

Degree: PhD, Physics, 2004, Penn State University

URL: https://etda.libraries.psu.edu/catalog/6269

► We present here recent developments in the technique of singularity excision. With the ultimate goal of developing a generic code which will evolve single or… (more)

Subjects/Keywords: black holes; classical general relativity; numerical relativity; singularity excision

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APA (6^th Edition):

Smith, K. L. (2004). Dynamic Singularity Excision in Numerical Relativity. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/6269

Chicago Manual of Style (16^th Edition):

Smith, Kenneth Lee. “Dynamic Singularity Excision in Numerical Relativity.” 2004. Doctoral Dissertation, Penn State University. Accessed July 24, 2019. https://etda.libraries.psu.edu/catalog/6269.

MLA Handbook (7^th Edition):

Smith, Kenneth Lee. “Dynamic Singularity Excision in Numerical Relativity.” 2004. Web. 24 Jul 2019.

Vancouver:

Smith KL. Dynamic Singularity Excision in Numerical Relativity. [Internet] [Doctoral dissertation]. Penn State University; 2004. [cited 2019 Jul 24]. Available from: https://etda.libraries.psu.edu/catalog/6269.

Council of Science Editors:

Smith KL. Dynamic Singularity Excision in Numerical Relativity. [Doctoral Dissertation]. Penn State University; 2004. Available from: https://etda.libraries.psu.edu/catalog/6269

Victoria University of Wellington

25. Cattoen, Celine. Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology.

Degree: 2009, Victoria University of Wellington

URL: http://hdl.handle.net/10063/972

► Cosmography is the part of cosmology that proceeds by making minimal dynamic assumptions. That is, one does not assume the Friedmann equations (Einstein equations) unless… (more)

▼ Cosmography is the part of cosmology that proceeds by making minimal dynamic assumptions. That is, one does not assume the Friedmann equations (Einstein equations) unless and until absolutely necessary. On the other hand, cosmodynamics is the part of cosmology that relates the geometry to the density and pressure using the Friedmann equations. In both frameworks, we consider the amount of information and the nature of the constraints we can obtain from the Hubble flow in a FLRW universe. Indeed, the cosmological parameters contained in the Hubble relation between distance and redshift provide information on the behaviour of the universe (expansion, acceleration etc...). In the first framework, it is possible to concentrate more directly on the observational situation in a model-independent manner. We perform a number of inter-related cosmographic fits to supernova datasets, and pay particular attention to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. In the second framework, we use the class of w-parameter models which has become increasingly popular in the last decade. We explore the extent to which a constraint on the w-parameter leads to useful and non-trivial constraints on the Hubble flow in terms of cosmological parameters H(z), density p(z), density parameter O(z), distance scales d(z), and lookback time T(z). On another front, Numerical Relativity has experienced many breakthroughs since 2005, with full inspiral-merger-ringdown simulations now possible. One of the main goals is to provide very accurate templates of gravitational waves for ground-based and space-based interferometers. We explore the potential of a very recent and accurate numerical method, the Spectral Element Method (SEM), for Numerical Relativity, by treating a singular Schwarszchild black hole evolution as a test case. Spectral elements combine the theory of spectral and pseudo-spectral methods for high order polynomials and the variational formulation of finite elements and the associated geometric flexibility. We use the BSSN formulation of the Einstein equations with the method of the moving punctures. After applying the variational formulation to the BSSN system, we present several possible weak forms of this system and its spectral element discretization in space. We use a Runge-Kutta fourth order time discretization. The accuracy of high order methods can deteriorate in the presence of discontinuities or sharp gradients. We show that we can treat the element that contains the puncture with a filtering method to avoid artificial and spurious oscillations. These might form and propagate into the domain coming from discontinuous initial data from the BSSN system. Advisors/Committee Members: Visser, Matt.

Subjects/Keywords: General relativity; Cosmology; Numerical relativity; Spectral element method

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APA (6^th Edition):

Cattoen, C. (2009). Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology. (Doctoral Dissertation). Victoria University of Wellington. Retrieved from http://hdl.handle.net/10063/972

Chicago Manual of Style (16^th Edition):

Cattoen, Celine. “Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology.” 2009. Doctoral Dissertation, Victoria University of Wellington. Accessed July 24, 2019. http://hdl.handle.net/10063/972.

MLA Handbook (7^th Edition):

Cattoen, Celine. “Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology.” 2009. Web. 24 Jul 2019.

Vancouver:

Cattoen C. Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology. [Internet] [Doctoral dissertation]. Victoria University of Wellington; 2009. [cited 2019 Jul 24]. Available from: http://hdl.handle.net/10063/972.

Council of Science Editors:

Cattoen C. Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology. [Doctoral Dissertation]. Victoria University of Wellington; 2009. Available from: http://hdl.handle.net/10063/972

Syracuse University

26. Kumar, Prayush. Topics in Gravitational-Wave Astrophysics.

Degree: PhD, Physics, 2014, Syracuse University

URL: https://surface.syr.edu/etd/173

► In this dissertation we study the applicability of different waveform models in gravitational wave searches for comparable mass binary black holes. We determine the… (more)

Subjects/Keywords: Black holes; Gravitational waves; Gravity; LIGO; Numerical Relativity; post-Newtonian; Physical Sciences and Mathematics

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APA (6^th Edition):

Kumar, P. (2014). Topics in Gravitational-Wave Astrophysics. (Doctoral Dissertation). Syracuse University. Retrieved from https://surface.syr.edu/etd/173

Chicago Manual of Style (16^th Edition):

Kumar, Prayush. “Topics in Gravitational-Wave Astrophysics.” 2014. Doctoral Dissertation, Syracuse University. Accessed July 24, 2019. https://surface.syr.edu/etd/173.

MLA Handbook (7^th Edition):

Kumar, Prayush. “Topics in Gravitational-Wave Astrophysics.” 2014. Web. 24 Jul 2019.

Vancouver:

Kumar P. Topics in Gravitational-Wave Astrophysics. [Internet] [Doctoral dissertation]. Syracuse University; 2014. [cited 2019 Jul 24]. Available from: https://surface.syr.edu/etd/173.

Council of Science Editors:

Kumar P. Topics in Gravitational-Wave Astrophysics. [Doctoral Dissertation]. Syracuse University; 2014. Available from: https://surface.syr.edu/etd/173

27. Mewes, Vassilios. Numerical relativity simulations of tilted black hole-torus systems.

Degree: 2018, TDX

URL: http://hdl.handle.net/10803/571049

► Mergers of compact objects are among the most interesting events of relativistic astrophysics, being, in particular, the prime target for gravitational wave astronomy. In this… (more)

▼ Mergers of compact objects are among the most interesting events of relativistic astrophysics, being, in particular, the prime target for gravitational wave astronomy. In this thesis, we investigate the possible end-states of black hole-neutron star and binary neutron star mergers: thick accretion tori around spinning Kerr black holes. These black hole-torus systems are believed to be the engines of the brightest events in the Universe, so-called gamma-ray bursts. Our understanding of the evolution and stability of these systems relies crucially on accurate numerical relativity simulations of their dynamics, evolving both spacetime and matter fields. The main work in this thesis are such numerical relativity simulations of black hole – torus systems. We use equilibrium models of self-gravitating discs around black holes as initial data, which represent idealised (yet relevant) models of the actual post-merger discs found in self-consistent numerical relativity merger simulations. Traditionally, numerical simulations of these systems have been carried out under the assumption that the black hole spin and disc angular momentum are aligned. There are arguments, however, that many black hole-torus systems should be tilted instead, which means that the equatorial plane of the disc is no longer parallel to that of the black hole. These tilted black hole-torus systems form indeed self-consistently in numerical relativity simulations of misaligned black hole-neutron star mergers. In these tilted systems, the dynamics of the torus and black hole change completely as compared to the untilted case due to general relativistic effects arising from the structure of the Kerr spacetime. Specifically, due to differential Lense-Thirring precession, the disc may become twisted and warped. To capture the correct dynamical response of these effects on the disc evolution, it is therefore necessary to evolve the systems in general relativistic hydrodynamics simulations. Pioneering work in this field has been carried out by Fragile and collaborators, who performed the first relativistic simulations of tilted black hole-torus systems in the test-fluid approximation, which means that the spacetime was held fixed in time and the self-gravity of the disc ignored. Building on this seminal work, we have performed in this thesis the first systematic study of tilted black hole-torus systems with a fully evolved spacetime. We observe many of the disc morphological features described in the test-fluid simulations of Fragile and collaborators. Additionally, we observe significant black hole precession and nutation as a result of the tilted disc evolution for all disc-to-black hole mass ratios considered in this thesis. The black hole spin direction is measured using a standard method in numerical relativity, which, as we show in this thesis, can be derived from Weinberg's pseudotensor. The black hole precession is seen to arise from the torque the disc exerts as it starts to precess… Advisors/Committee Members: Font Roda, José Antonio, Montero Muriel, Pedro J., Departament d'Astronomia i Astrofísica.

Subjects/Keywords: accretion, accretion discs; black hole physics; hydrodynamics; instabilities; numerical relativity; UNESCO::ASTRONOMÍA Y ASTROFÍSICA

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APA (6^th Edition):

Mewes, V. (2018). Numerical relativity simulations of tilted black hole-torus systems. (Thesis). TDX. Retrieved from http://hdl.handle.net/10803/571049

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mewes, Vassilios. “Numerical relativity simulations of tilted black hole-torus systems.” 2018. Thesis, TDX. Accessed July 24, 2019. http://hdl.handle.net/10803/571049.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mewes, Vassilios. “Numerical relativity simulations of tilted black hole-torus systems.” 2018. Web. 24 Jul 2019.

Vancouver:

Mewes V. Numerical relativity simulations of tilted black hole-torus systems. [Internet] [Thesis]. TDX; 2018. [cited 2019 Jul 24]. Available from: http://hdl.handle.net/10803/571049.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mewes V. Numerical relativity simulations of tilted black hole-torus systems. [Thesis]. TDX; 2018. Available from: http://hdl.handle.net/10803/571049

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

28. Lopez-Aleman, Ramon. EVOLVING PARTICLE TRAJECTORIES PERTURBATIVELY AROUND ROTATING BLACK HOLES IN THE TIME DOMAIN.

Degree: PhD, Physics, 2001, Penn State University

URL: https://etda.libraries.psu.edu/catalog/5862

► Treating the Teukolsky perturbation equation numerically as a 2+1 PDE and smearing the singularities in the particle source term by the use of narrow gaussian… (more)

Subjects/Keywords: perturbation theory; black holes; Numerical Relativity

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APA (6^th Edition):

Lopez-Aleman, R. (2001). EVOLVING PARTICLE TRAJECTORIES PERTURBATIVELY AROUND ROTATING BLACK HOLES IN THE TIME DOMAIN. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/5862

Chicago Manual of Style (16^th Edition):

Lopez-Aleman, Ramon. “EVOLVING PARTICLE TRAJECTORIES PERTURBATIVELY AROUND ROTATING BLACK HOLES IN THE TIME DOMAIN.” 2001. Doctoral Dissertation, Penn State University. Accessed July 24, 2019. https://etda.libraries.psu.edu/catalog/5862.

MLA Handbook (7^th Edition):

Lopez-Aleman, Ramon. “EVOLVING PARTICLE TRAJECTORIES PERTURBATIVELY AROUND ROTATING BLACK HOLES IN THE TIME DOMAIN.” 2001. Web. 24 Jul 2019.

Vancouver:

Lopez-Aleman R. EVOLVING PARTICLE TRAJECTORIES PERTURBATIVELY AROUND ROTATING BLACK HOLES IN THE TIME DOMAIN. [Internet] [Doctoral dissertation]. Penn State University; 2001. [cited 2019 Jul 24]. Available from: https://etda.libraries.psu.edu/catalog/5862.

Council of Science Editors:

Lopez-Aleman R. EVOLVING PARTICLE TRAJECTORIES PERTURBATIVELY AROUND ROTATING BLACK HOLES IN THE TIME DOMAIN. [Doctoral Dissertation]. Penn State University; 2001. Available from: https://etda.libraries.psu.edu/catalog/5862

Penn State University

29. Vaishnav, Birjoo. Gravitational waves from Intermediate Mass Binary Black Holes: First steps toward using Numerical Relativity waveforms for LIGO data analysis.

Degree: PhD, Physics, 2008, Penn State University

URL: https://etda.libraries.psu.edu/catalog/8821

► The need for providing accurate and reliable templates for detecting gravitational waves from the LIGO and LISA gravity wave detectors has fueled the numerical relativity… (more)

Subjects/Keywords: black holes; gravitational waves; numerical relativity; LIGO; data analysis; gravitational wave astronomy

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APA (6^th Edition):

Vaishnav, B. (2008). Gravitational waves from Intermediate Mass Binary Black Holes: First steps toward using Numerical Relativity waveforms for LIGO data analysis. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/8821

Chicago Manual of Style (16^th Edition):

Vaishnav, Birjoo. “Gravitational waves from Intermediate Mass Binary Black Holes: First steps toward using Numerical Relativity waveforms for LIGO data analysis.” 2008. Doctoral Dissertation, Penn State University. Accessed July 24, 2019. https://etda.libraries.psu.edu/catalog/8821.

MLA Handbook (7^th Edition):

Vaishnav, Birjoo. “Gravitational waves from Intermediate Mass Binary Black Holes: First steps toward using Numerical Relativity waveforms for LIGO data analysis.” 2008. Web. 24 Jul 2019.

Vancouver:

Vaishnav B. Gravitational waves from Intermediate Mass Binary Black Holes: First steps toward using Numerical Relativity waveforms for LIGO data analysis. [Internet] [Doctoral dissertation]. Penn State University; 2008. [cited 2019 Jul 24]. Available from: https://etda.libraries.psu.edu/catalog/8821.

Council of Science Editors:

Vaishnav B. Gravitational waves from Intermediate Mass Binary Black Holes: First steps toward using Numerical Relativity waveforms for LIGO data analysis. [Doctoral Dissertation]. Penn State University; 2008. Available from: https://etda.libraries.psu.edu/catalog/8821

University of Otago

30. Escobar , Leon. Studies of spacetimes with spatial topologies S3 and S1 X S2 .

Degree: University of Otago

URL: http://hdl.handle.net/10523/6451

► The purpose of this work is to introduce a new analytical and numerical approach to the treatment of the initial value problem for the vacuum… (more)

▼ The purpose of this work is to introduce a new analytical and numerical approach to the treatment of the initial value problem for the vacuum Einstein field equations on spacetimes with spatial topologies S3 or S1 × S2 and symmetry groups U(1) or U(1)×U(1). The general idea consists of taking advantage of the action of the symmetry group U(1) to rewrite those spacetimes as a principal fiber bundle, which is trivial for S1 × S2 but not for S3. Thus, the initial value problem in four dimensions can be reduced to a three-dimensional initial value problem for a certain manifold with spatial topology S2. Furthermore, we avoid coordinate representations that suffer from coordinate singularities for S2 by expressing all the fields in terms of the spin-weighted spherical harmonics. We use the generalized wave map formalism to reduce the vacuum Einstein field equations on a manifold with three spatial dimensions to a system of quasilinear wave equations in terms of generalized gauge source functions with well-defined spin-weights. As a result, thanks to the fully tensorial character of these equations, the system of evolution equations can be solved numerically using a 2 + 1-pseudo-spectral approach based on a spin-weighted spherical harmonic transform. In this work, however, we apply our infrastructure to the study of Gowdy symmetric spacetimes, where thanks to the symmetry group U(1) × U(1), the system of hyperbolic equations obtained from the vacuum Einstein field equations can be reduced to a 1+1-system of partial differential equations. Therefore, we introduce an axial symmetric spin-weighted transform that provides an efficient treatment of axially symmetric functions in S2 by reducing the complexity of the general transform. To analyse the consistency, accuracy, and feasibility of our numerical infrastructure, we reproduce an inhomogeneous cosmological solution of the vacuum Einstein field quations with spatial topology S3 . In addition, we consider two applications of our infrastructure. In the first one, we numerically explore the behaviour of Gowdy S1 × S2 spacetimes using our infrastructure. In particular, we study the behaviour of some geometrical quantities to investigate the behaviour of those spacetimes when approach a future singularity. As a second application, we conduct a systematic investigation on the non-linear instability of the Nariai spacetime and the asymptotic behaviour of its perturbations. Advisors/Committee Members: Frauendiener, Jorg (advisor).

Subjects/Keywords: Relativity; Spectral; Spherical; Gowdy; Numerical; Spacetimes

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APA (6^th Edition):

Escobar , L. (n.d.). Studies of spacetimes with spatial topologies S3 and S1 X S2 . (Doctoral Dissertation). University of Otago. Retrieved from http://hdl.handle.net/10523/6451

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Chicago Manual of Style (16^th Edition):

Escobar , Leon. “Studies of spacetimes with spatial topologies S3 and S1 X S2 .” Doctoral Dissertation, University of Otago. Accessed July 24, 2019. http://hdl.handle.net/10523/6451.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

MLA Handbook (7^th Edition):

Escobar , Leon. “Studies of spacetimes with spatial topologies S3 and S1 X S2 .” Web. 24 Jul 2019.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Vancouver:

Escobar L. Studies of spacetimes with spatial topologies S3 and S1 X S2 . [Internet] [Doctoral dissertation]. University of Otago; [cited 2019 Jul 24]. Available from: http://hdl.handle.net/10523/6451.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Council of Science Editors:

Escobar L. Studies of spacetimes with spatial topologies S3 and S1 X S2 . [Doctoral Dissertation]. University of Otago; Available from: http://hdl.handle.net/10523/6451

Note: this citation may be lacking information needed for this citation format:
No year of publication.

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