The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse
Journal article, 2010

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.


Håkan Andreasson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Gerhard Rein

University of Bayreuth

Mathematical Proceedings of the Cambridge Philosophical Society

0305-0041 (ISSN) 1469-8064 (eISSN)

Vol. 149 1 173-188

Subject Categories

Computational Mathematics

Astronomy, Astrophysics and Cosmology

Mathematical Analysis



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