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The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse

Published online by Cambridge University Press:  05 January 2010

HÅKAN ANDRÉASSON  and
GERHARD REIN
HÅKAN ANDRÉASSON
Affiliation:
Mathematical Sciences, University of Gothenburg, Mathematical Sciences, Chalmers University of Technology, S-41296 Göteborg, Sweden. e-mail: hand@chalmers.se
GERHARD REIN
Affiliation:
Mathematisches Institut der Universität Bayreuth, D-95440 Bayreuth, Germany. e-mail: gerhard.rein@uni-bayreuth.de
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Abstract

Given a static Schwarzschild spacetime of ADM mass M, it is well known that no ingoing causal geodesic starting in the outer domain r > 2M will cross the event horizon r = 2M in finite Schwarzschild time. We show that in gravitational collapse of Vlasov matter this behaviour can be very different. We construct initial data for which a black hole forms and all matter crosses the event horizon as Schwarzschild time goes to infinity, and show that this is a necessary condition for geodesic completeness of the event horizon. In addition to a careful analysis of the asymptotic behaviour of the matter characteristics our proof requires a new argument for global existence of solutions to the spherically symmetric Einstein–Vlasov system in an outer domain, since our initial data have non-compact support in the radial momentum variable and previous methods break down.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 173 - 188
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

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