Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-02-24
Math.Proc.Cambridge Phil.Soc.149:173-188,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages
Scientific paper
10.1017/S0305004109990454
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.
Andreasson Hakan
Rein Gerhard
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