The University of Southampton
University of Southampton Institutional Repository

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
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). (doi:10.1103/PhysRevD.96.084008).

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
Download (746kB)

More information

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 iD orcid.org/0000-0001-9585-5375

Catalogue record

Date deposited: 31 Oct 2017 17:30
Last modified: 20 Jul 2018 00:34

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×