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Showing 1 to 20 of 42 for “"Schwarzschild"”.
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Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes
I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish …
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An Analogue of the Laplace-Runge-Lenz Vector for Timelike Geodesics in Schwarzschild Spacetime
In Schwarzschild spacetime, the timelike geodesics are the trajectories of free, massive particles, orbiting a singularity at the origin r = 0. In this work we derive four scalar first integrals of timelike geodesics in Schwarzschild spacetime. Two of the first integrals, corresponding to energy …
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A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole
… for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We perform this construction in two parts. In Part I, we construct a scattering theory for the spin ±2 Teukolsky equations, which govern certain the extremal, gauge-invariant components of the …
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A imagem de um buraco negro: um estudo das geodésicas tipo-luz no espaço-tempo de Schwarzschild
… e extremante eficiente baseada na métrica de Schwarzschild. Analisando um buraco negro estático e esfericamente simétrico, é possível usar tal ferramenta para descrever a influência desse corpo sobre o espaço-tempo ao seu redor. A partir da relação entre a deformação pela gravidade e o …
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Signature change in spherical vacuum spacetimes
… The metrics we chose to investigate are the Schwarzschild metric and the Tolman metric. The Schwarzschild metric was originally chosen in order to investigate whether the neighborhood of the singularity inside a black hole can be replaced with a Euclidean region, and also to see whether this …
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The Gregory--Laflamme Instability and Conservation Laws for Linearised Gravity
… instability for the 5-dimensional Schwarzschild black string. Under a choice of ansatz for the perturbation and a gauge choice, the linearised vacuum Einstein equation reduces to an ODE problem for a single function. In this work, the ODE is cast into a Schrödinger eigenvalue …
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Total mass of a patch of a matter-dominated Friedmann-Robertson-Walker universe
… surrounded with a vacuum described by the Schwarzschild metric. Provided that the patch of FRW spacetime is glued along its boundary to a Schwarzschild spacetime in a sufficiently smooth manner, the result is a spatial region of FRW which transitions smoothly to an asymptotically flat …
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Fermion Quantum Field Theory In Black-hole Spacetimes
… the theory of free fermions living on the static Schwarzschild black-hole and the rotating Kerr black-hole. The construction capitalises upon the fact that both black-holes are stationary axisymmetric solutions to Einstein's equation. A factorisability ansatz is developed whereby simple quantum …
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A Numerical Study of Three-Dimensional Black Hole Spacetimes
… 3D Cartesian coordinates. We first studied the Schwarzschild spacetime, comparing extensively with 1D studies. We show that although accurate 3D evolutions are possible, there are a number of difficulties in evolving 3D black holes, for which we suggest approaches to overcome. With current …
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A numerical study of 3D black hole spacetimes
… 3D Cartesian coordinates. We first studied the Schwarzschild spacetime, comparing extensively with lD studies. We show that although accurate 3D evolutions are possible, there are a number of difficulties in evolving 3D black holes, for which we suggest approaches to overcome. With current …
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Gravitational lensing
… of massive dark objects at galactic center as Schwarzschild black hole lenses. We also demonstrate the gravitational lensing analysis in f(R) gravity theories.
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Discrete gravitational approaches to cosmology
… 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 …
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Ricci Curvature of Finsler Metrics by Warped Product
… over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with …
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Leveraging numerical relativity formulations for perturbative analysis: applications to quasinormal modes in general relativity
… for analyzing linearized perturbations of a Schwarzschild black hole using the characteristic formulation of numerical relativity, focusing on the computation of quasinormal modes (QNMs). Unlike traditional methods based on the Regge-Wheeler and Zerilli equations, this approach focuses on …
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Defining gravitational singularities in general relativity
… including Friedman-Lemaitre-Robertson-Walker, Schwarzschild, self-similar Vaidya, self-similar Tolman-Bondi, non-self-similar Vaidya, and Kerr spacetimes. We find that in every case studied, the integral curves have specific end points, therefore they can be used to classify a curvature …
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Numerical relativity from a gauge theory perspective
… a weak gravitational wave spacetime, the Schwarzschild spacetime, and the Kerr spacetime.
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Linear and non-linear collisionless many-particle systems
… a non-linear asymptotic stability result of the Schwarzschild family of black holes as solutions to the spherically symmetric Einstein--massless Vlasov system in the exterior of the black hole region. The proof exploits the normal hyperbolicity of the null geodesic flow in a neighborhood of the …
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Decay for quasilinear wave equations on cosmological black hole backgrounds
… of linear and quasilinear wave equations of Schwarzschild--de~Sitter $(M,\Lambda)$ and Kerr de Sitter $(a,M,\Lambda)$ black hole backgrounds, where $a,M,\Lambda$ are respectively the rotation parameter of the black hole, the mass of the black hole and the cosmological constant. Specifically, …
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On Stability and Evolution of Solutions in General Relativity
… investigate the evolutionary linear stability of Schwarzschild-like solutions in higher dimensional relativity called black strings. These objects are determined to be linearly unstable. This motivates a further stability analysis of the charged p-brane solutions of low energy string theory. We …
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Givenness, focus, and prosody
… and the inseparable phenomenon of givenness. As Schwarzschild (1999) has proposed, a proper understanding of givenness eliminates the need for a separate concept of focus, which is notoriously hard to define, either semantically, syntactically, or phonologically. I propose a semantic constraint, …
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