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

Abstract

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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References in corpus (4)

• On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
• The formation of black holes in spherically symmetric gravitational collapse
• Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
• The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse

Cited by in corpus (8)

• The Einstein-Vlasov System/Kinetic Theory
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter
• The formation of trapped surfaces in spherically-symmetric Einstein-Euler spacetimes with bounded variation
• On the small redshift limit of steady states of the spherically symmetric Einstein-Vlasov system and their stability
• A numerical stability analysis for the Einstein-Vlasov system
• Spherical accretion of a collisionless kinetic gas into a generic static black hole
• Initial data and black holes for matter models
• Gravitational collapse in the vicinity of the extremal black hole critical point