The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions
The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions
We reduce the equations governing the spherically symmetric perturbations of static spherically symmetric solutions of the Einstein-Vlasov system (with either massive or massless particles) to a single stratified wave equation $-\psi_{,tt}=H\psi$, with $H$ containing second derivatives in radius, and integrals over energy and angular momentum. We identify an inner product with respect to which $H$ is symmetric, and use the Ritz method to approximate the lowest eigenvalues of $H$ numerically. For two representative background solutions with massless particles we find a single unstable mode with a growth rate consistent with the universal one found by Akbarian and Choptuik in nonlinear numerical time evolutions.
gr-qc
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Gundlach, Carsten
(2017)
The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions.
Physical Review D, 96 (8), [084008].
(doi:10.1103/PhysRevD.96.084008).
Abstract
We reduce the equations governing the spherically symmetric perturbations of static spherically symmetric solutions of the Einstein-Vlasov system (with either massive or massless particles) to a single stratified wave equation $-\psi_{,tt}=H\psi$, with $H$ containing second derivatives in radius, and integrals over energy and angular momentum. We identify an inner product with respect to which $H$ is symmetric, and use the Ritz method to approximate the lowest eigenvalues of $H$ numerically. For two representative background solutions with massless particles we find a single unstable mode with a growth rate consistent with the universal one found by Akbarian and Choptuik in nonlinear numerical time evolutions.
Text
1708.07191
- Accepted Manuscript
More information
Accepted/In Press date: 14 September 2017
e-pub ahead of print date: 4 October 2017
Keywords:
gr-qc
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Local EPrints ID: 415120
URI: http://eprints.soton.ac.uk/id/eprint/415120
PURE UUID: 5b6927ca-382b-4436-bc19-e46e783aa405
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Date deposited: 31 Oct 2017 17:30
Last modified: 16 Mar 2024 03:15
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