Existence of Static Solutions of the Einstein-Vlasov-Maxwell System and the Thin Shell Limit

TL;DR

This paper proves the existence of static solutions in the Einstein-Vlasov-Maxwell system with spherical symmetry, including the thin shell limit, and establishes a sharp Buchdahl-type inequality relating radius, charge, and mass.

Contribution

It demonstrates local and global existence of solutions with bounded support and analyzes the thin shell limit, extending previous inequalities to include charge effects.

Findings

Existence of static solutions around the center of symmetry.

Global solutions for small particle charges.

Thin shell limit exists for arbitrary charge values.

Abstract

In this article the static Einstein-Vlasov-Maxwell system is considered in spherical symmetry. This system describes an ensemble of charged particles interacting by general relativistic gravity and Coulomb forces. First, a proof for local existence of solutions around the center of symmetry is given. Then, by virtue of a perturbation argument, global existence is established for small particle charges. The method of proof yields solutions with matter quantities of bounded support - among other classes, shells of charged Vlasov matter. As a further result, the limit of infinitesimal thin shells as solution of the Einstein-Vlasov-Maxwell system is proven to exist for arbitrary values of the particle charge parameter. In this limit a Buchdahl-type inequality linking radius, charge and Hawking mass, obtained by Andreasson becomes sharp. However, in this limit the charge terms in the inequality are shown to tend to zero.