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Existence of static solutions of the Einstein-vlasov-maxwell system and the thin shell limit

Journal article
Authors Maximilian Thaller
Published in SIAM Journal on Mathematical Analysis
Volume 51
Issue 3
Pages 2231-2260
ISSN 0036-1410
Publication year 2019
Published at Department of Mathematical Sciences
Pages 2231-2260
Language en
Keywords Buchdahl inequality, Einstein equations, Einstein-Vlasov-Maxwell system, static solutions, thin shell limit, Charged particles, Shells (structures), Vlasov equation, Thin shells, Vlasov-Maxwell system, Maxwell equations
Subject categories Mathematics


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 infinitesimally 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 the inequality which has been obtained by Andrèasson in [Comm. Math. Phys., 288 (2009), pp. 715-730], and which bounds the mass-toradius ratio by a constant and the charge-to-radius ratio, becomes sharp. However, in this limit the charge terms in the inequality are shown to tend to zero. © 2019 SIAM.

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