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 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.
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Binney, J., Tremaine, S.: Galactic Dynamics, 2nd edn. Princeton University Press, Princeton 2008
Rein, G.: Collisionless kinetic equations from astrophysics—the Vlasov–Poisson system. In: Dafermos, C., Feireisl, E. (eds.) Handbook of Differential Equations, Evolutionary Equations, vol. 3, pp. 383–476. Elsevier, London 2007
Wolansky, G.: Static solutions of the Vlasov–Einstein system. Arch. Ration. Mech. Anal. 156, 205–230, 2001
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Communicated by N. Masmoudi
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Andréasson, H., Kunze, M. Comments on the paper ‘Static solutions of the Vlasov–Einstein system’ by G. Wolansky. Arch Rational Mech Anal 235, 783–791 (2020). https://doi.org/10.1007/s00205-019-01432-2
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DOI: https://doi.org/10.1007/s00205-019-01432-2