Universität zu Köln

Andreasson, Hakan and Kunze, Markus (2020). Comments on the paper 'Static solutions of the Vlasov-Einstein system' by G. Wolansky. Arch. Ration. Mech. Anal., 235 (1). S. 783 - 792. NEW YORK: SPRINGER. ISSN 1432-0673

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Abstract

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 showthat 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Andreasson, Hakan UNSPECIFIED UNSPECIFIED UNSPECIFIED Kunze, Markus UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-351173
DOI:	10.1007/s00205-019-01432-2
Journal or Publication Title:	Arch. Ration. Mech. Anal.
Volume:	235
Number:	1
Page Range:	S. 783 - 792
Date:	2020
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0673
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics, Applied; Mechanics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/35117