Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole

TL;DR

This paper demonstrates the existence of static, shell-like solutions to the massless Einstein-Vlasov system that can surround a Schwarzschild black hole, including multiple well-separated shells, supported by both analytical proofs and numerical analysis.

Contribution

It provides the first known static self-gravitating solutions of a massless Einstein-matter system surrounding a black hole, with proofs and numerical insights.

Findings

Existence of steady shell solutions around a Schwarzschild black hole.

Multiple well-separated shells can surround the black hole.

Numerical investigation of shell properties.

Abstract

We show that there exist steady states of the massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole. To our knowledge this is the first result of static self-gravitating solutions to any massless Einstein-matter system which surround a black hole. We also include a numerical investigation about the properties of the shells.