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arXiv · 0902.4097

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

Hakan Andreasson·Gerhard Rein
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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. In the present paper 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 we 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.

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Hakan Andreasson, Gerhard Rein. 2009-02-24. The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse. https://doi.org/10.1017/s0305004109990454

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