Extremal black hole formation as a critical phenomenon

TL;DR

This paper rigorously demonstrates that extremal black holes form at the threshold of gravitational collapse in a spherically symmetric Einstein-Maxwell-Vlasov system, revealing a new critical phenomenon in general relativity.

Contribution

It provides the first rigorous proof of extremal black hole formation at the collapse threshold in Einstein-Maxwell-Vlasov systems, introducing the concept of extremal critical collapse.

Findings

Extremal black holes arise at the collapse threshold.

Solutions interpolate between dispersion and collapse.

No naked singularities occur at the threshold.

Abstract

In this paper, we prove that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal black hole. Physically, these solutions can be understood as beams of gravitationally self-interacting collisionless charged particles fired into Minkowski space from past infinity. Depending on the precise value of the parameter, we show that the Vlasov matter either disperses due to the combined effects of angular momentum and electromagnetic repulsion, or undergoes gravitational collapse. At the critical value of the parameter, an extremal Reissner-Nordstr\"om black hole is formed. No naked singularities occur as the extremal threshold is crossed. We call this critical phenomenon extremal critical collapse and the present work constitutes the first rigorous result on the black hole formation threshold in general relativity.