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Comments on the paper ‘Static solutions of the Vlasov–Einstein system’ by G. Wolansky

Editorial letter
Authors Håkan Andréasson
Published in Archive for Rational Mechanics and Analysis
ISSN 0003-9527
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Subject categories Mathematics


In this note we address the attempted proof of the existence of static solutions to the Einstein–Vlasov system as given in Wolansky (Arch Ration Mech Anal 156:205–230, 2001). We focus on a specific and central part of the proof which concerns a variational problem with an obstacle. We show that two important claims in Wolansky (2001) are incorrect and we question the validity of a third claim. We also discuss the variational problem and its difficulties with the aim of stimulating further investigation of this intriguing problem in particular answering the question of whether or not static solutions of the Einstein–Vlasov system can be found as local minimizers of an energy-Casimir functional. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

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