An extension principle for the Einstein-Vlasov system in spherical symmetry

TL;DR

This paper proves that the earliest singularities in spherically symmetric Einstein-Vlasov systems originate at the center, providing insights into black hole formation and weak cosmic censorship in collisionless matter collapse.

Contribution

It establishes that first singularities must emanate from the center in spherically symmetric Einstein-Vlasov systems, advancing understanding of singularity formation and cosmic censorship.

Findings

First singularities originate from the center

Provides a framework for weak cosmic censorship

Proves black hole formation from regular initial data

Abstract

We prove that "first singularities" in the non-trapped region of the maximal development of spherically symmetric asymptotically flat data for the Einstein-Vlasov system must necessarily emanate from the center. The notion of "first" depends only on the causal structure and can be described in the language of terminal indecomposable pasts (TIPs). This result suggests a local approach to proving weak cosmic censorship for this system. It can also be used to give the first proof of the formation of black holes by the collapse of collisionless matter from regular initial configurations.