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Models for Self-Gravitating Photon Shells and Geons

Journal article
Authors Håkan Andreasson
D. Fajman
Maximilian Thaller
Published in Annales Henri Poincare
Volume 18
Issue 2
Pages 681-705
ISSN 1424-0637
Publication year 2017
Published at Department of Mathematical Sciences
Pages 681-705
Language en
Keywords einstein-vlasov system, spherically symmetric equilibria, smooth static, solutions, yang-mills equations, collisionless matter, buchdahl, inequality, general-relativity, steady-states, existence, Physics
Subject categories Physical Sciences


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.

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