Rotating Clouds of Charged Vlasov Matter in General Relativity

Abstract

The existence of stationary solutions of the Einstein-Vlasov-Maxwell system which are axially symmetric but not spherically symmetric is proven by means of the implicit function theorem on Banach spaces. The proof generalises the methods of an article by Håkan Andréasson, Markus Kunze and Gerhard Rein where a similar result is obtained for uncharged particles. Among the solutions constructed in this article there are rotating and non-rotating ones. Static solutions exhibit an electric but no magnetic field. In the case of rotating solutions, in addition to the electric field, a purely poloidal magnetic field is induced by the particle current. The existence of toroidal components of the magnetic field turns out to be not possible in this setting.

arXiv comment32 pages

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Cited by in corpus (4)

• An introduction to the relativistic kinetic theory on curved spacetimes
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• Einstein-Vlasov system with equal-angular momenta in ${\text{AdS}}_5$