Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system
Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a curvature singularity by construction, and their initial data on a Cauchy surface to the past of the singularity can be chosen to have compact support in momentum space. They can also be truncated at large radius so that they have compact support in space, while retaining self-similarity in a central region that includes the singularity. However, the Vlasov distribution function cannot be bounded. As a simpler illustration of our techniques and notation we also construct the general spherically symmetric and static solution, for both massive and massless particles.
084062-[18pp]
Martin-Garcia, Jose M.
b7d735d1-2f76-4585-927d-ac868cc6bd90
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
15 April 2002
Martin-Garcia, Jose M.
b7d735d1-2f76-4585-927d-ac868cc6bd90
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Martin-Garcia, Jose M. and Gundlach, Carsten
(2002)
Self-similar spherically symmetric solutions of the massless Einstein-Vlasov system.
Physical Review D, 65 (8), .
(doi:10.1103/PhysRevD.65.084026).
Abstract
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a curvature singularity by construction, and their initial data on a Cauchy surface to the past of the singularity can be chosen to have compact support in momentum space. They can also be truncated at large radius so that they have compact support in space, while retaining self-similarity in a central region that includes the singularity. However, the Vlasov distribution function cannot be bounded. As a simpler illustration of our techniques and notation we also construct the general spherically symmetric and static solution, for both massive and massless particles.
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Published date: 15 April 2002
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Local EPrints ID: 29191
URI: http://eprints.soton.ac.uk/id/eprint/29191
ISSN: 1550-7998
PURE UUID: 1b84ef16-18ca-4bf2-a565-f180af12c280
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 03:15
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Author:
Jose M. Martin-Garcia
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