In this note we address the attempted proof of the existence of static solutions to the Einstein-Vlasov system as given in \cite{ Wol}. 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 \cite{ Wol} are incorrect and we question the validity of a third claim. We also discuss the variational problem and its difficulties with the aim to stimulate further investigations of this intriguing problem: to answer the question whether or not static solutions of the Einstein-Vlasov system can be found as local minimizers of an energy-Casimir functional.
Categories: gr-qc math.AP