Comments on the paper 'Static solutions of the Vlasov-Einstein system' by G. Wolansky

被引：2

作者：

Andreasson, Hakan ^{[1
]}

Kunze, Markus ^{[2
]}

机构：

[1] Gothenburg Univ, Chalmers Univ Technol, Math Sci, S-41296 Gothenburg, Sweden

[2] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2020年 / 235卷 / 01期

关键词：

D O I：

10.1007/s00205-019-01432-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：783 / 791

页数：9