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# The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions

Gundlach, Carsten (2017) The Einstein-Vlasov system in spherical symmetry II: spherical perturbations of static solutions. Physical Review D, 96 (8).

Record type: Article

## 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

Accepted/In Press date: 14 September 2017
e-pub ahead of print date: 4 October 2017
Keywords: gr-qc

## Identifiers

Local EPrints ID: 415120
URI: https://eprints.soton.ac.uk/id/eprint/415120
PURE UUID: 5b6927ca-382b-4436-bc19-e46e783aa405
ORCID for Carsten Gundlach: orcid.org/0000-0001-9585-5375

## Catalogue record

Date deposited: 31 Oct 2017 17:30