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

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.