Comments on the paper ‘Static solutions of the Vlasov–Einstein system’ by G. Wolansky
Journal article, 2019

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.

Author

Håkan Andreasson

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Markus Kunze

University of Cologne

Archive for Rational Mechanics and Analysis

0003-9527 (ISSN) 1432-0673 (eISSN)

Subject Categories

Philosophy

Other Mathematics

Mathematical Analysis

DOI

10.1007/s00205-019-01432-2

More information

Latest update

11/7/2019