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

TL;DR

This paper establishes explicit initial data conditions for the formation of trapped surfaces in the spherically symmetric Einstein-Vlasov system, demonstrating implications for cosmic censorship and horizon behavior.

Contribution

It provides the first explicit criteria for trapped surface formation in Einstein-Vlasov systems and analyzes horizon dynamics post-formation.

Findings

Explicit initial data conditions for trapped surfaces

Event horizon is future complete

Apparent and event horizons do not coincide

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.