Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system

TL;DR

This paper reviews the Einstein-Vlasov system under spherical symmetry, highlighting conditions for black hole formation, and demonstrates that certain solutions satisfy cosmic censorship and contain black holes.

Contribution

It provides explicit initial data conditions guaranteeing black hole formation and shows these solutions satisfy weak cosmic censorship in the Einstein-Vlasov context.

Findings

Explicit initial data conditions for black hole formation

Solutions exist globally in Schwarzschild coordinates

Spacetimes satisfy weak cosmic censorship

Abstract

We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution. Among these data there are data such that the corresponding solutions exist globally in Schwarzschild coordinates. We put these results into a more general context, and we include arguments which show that the spacetimes we obtain satisfy the weak cosmic censorship conjecture and contain a black hole in the sense of suitable mathematical definitions of these concepts which are available in the literature.