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Showing 1 to 6 of 6 for “"Schwarzschild spacetime"”.
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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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Numerical relativity from a gauge theory perspective
… simulations of several analytically solvable spacetimes: a weak gravitational wave spacetime, the Schwarzschild spacetime, and the Kerr spacetime.
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Total mass of a patch of a matter-dominated Friedmann-Robertson-Walker universe
… of a spherically-symmetric matter-dominated spacetime of negative curvature. This calculation provides the open-universe analogue to a similar calculation first proposed by Zel'dovich in 1962. I consider a finite, spherically-symmetric (SO(3)) spatial region of a Friedmann-Robertson-Walker …
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A Numerical Study of Three-Dimensional Black Hole Spacetimes
… from numerical evolutions of vacuum black hole spacetimes in 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, …
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A numerical study of 3D black hole spacetimes
… from numerical evolutions of vacuum black hole spacetimes in 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, …
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Linear and non-linear collisionless many-particle systems
… systems in the exterior of black hole spacetimes. In Chapter 4, we prove 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 …