Black hole formation from a complete regular past for collisionless matter

TL;DR

This paper constructs initial data for the Einstein-Vlasov system demonstrating black hole formation from a regular past, showing such phenomena can occur with realistic matter models and that solutions can exist for all Schwarzschild times.

Contribution

It provides the first example of initial data with regular past evolution leading to black holes in the Einstein-matter system with realistic matter.

Findings

Existence of initial data with regular past and black hole future.

Black hole formation occurs even when the mass-to-radius ratio is arbitrarily small.

Solutions can exist for all Schwarzschild times, including negative infinity.

Abstract

Initial data for the spherically symmetric Einstein-Vlasov system is constructed whose past evolution is regular and whose future evolution contains a black hole. This is the first example of initial data with these properties for the Einstein-matter system with a "realistic" matter model. One consequence of the result is that there exists a class of initial data for which the ratio of the Hawking mass $\open{m}=\open{m}(r)$ and the area radius $r$ is arbitrarily small everywhere, such that a black hole forms in the evolution. This result is in a sense analogous to the result for a scalar field. Another consequence is that there exist black hole initial data such that the solutions exist for all Schwarzschild time $t\in (-\infty,\infty)$.