Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

Details Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system

2009-10-07

arxiv.org/abs/0910.1254v1

J.Hyperbol.Diff.Equat.7:707-731,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27

Scientific paper

10.1142/S0219891610002268

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington-Finkelstein coordinates.

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