Models for Self-Gravitating Photon Shells and Geons

TL;DR

This paper proves the existence of highly relativistic, spherically symmetric, static self-gravitating photon shells within the Einstein-Vlasov system, offering an alternative model to Wheeler's geons with solutions where the mass-to-radius ratio approaches 8/9.

Contribution

It introduces the first rigorous proof of self-gravitating photon shells as solutions to the Einstein-Vlasov system, expanding the theoretical understanding of geon-like structures.

Findings

Existence of spherically symmetric, static photon shells proved.

Solutions are highly relativistic with mass-to-radius ratio near 8/9.

Provides an alternative model for photon shells and geons.

Abstract

We prove existence of spherically symmetric, static, self-gravitating photon shells as solutions to the massless Einstein-Vlasov system. The solutions are highly relativistic in the sense that the ratio $2m(r)/r$ is close to $8/9$, where $m(r)$ is the Hawking mass and $r$ is the area radius. In 1955 Wheeler constructed, by numerical means, so called idealized spherically symmetric geons, i.e. solutions of the Einstein-Maxwell equations for which the energy momentum tensor is spherically symmetric on a time average. The structure of these solutions is such that the electromagnetic field is confined to a thin shell for which the ratio $2m/r$ is close to $8/9$, i.e., the solutions are highly relativistic photon shells. The solutions presented in this work provide an alternative model for photon shells or idealized spherically symmetric geons.