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- W4225662482 abstract "Existence of spherically symmetric solutions to the Einstein-Vlasov system is well-known. However, it is an open problem whether or not static solutions arise as minimizers of a variational problem. Apart from being of interest in its own right, it is the connection to non-linear stability that gives this topic its importance. This problem was considered in cite{Wol}, but as has been pointed out in cite{AK}, the paper cite{Wol} contained serious flaws. In this work we construct static solutions by solving the Euler-Lagrange equation for the energy density $rho$ as a fixed point problem. The Euler-Lagrange equation originates from the particle number-Casimir functional introduced in cite{Wol}. We then define a density function $f$ on phase space which induces the energy density $rho$ and we show that it constitutes a static solution of the Einstein-Vlasov system. Hence we settle rigorously parts of what the author of cite{Wol} attempted to prove." @default.
- W4225662482 created "2022-05-05" @default.
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- W4225662482 date "2022-02-03" @default.
- W4225662482 modified "2023-09-30" @default.
- W4225662482 title "Static solutions to the spherically symmetric Einstein-Vlasov system: a particle-number-Casimir approach" @default.
- W4225662482 doi "https://doi.org/10.48550/arxiv.2202.01835" @default.
- W4225662482 hasPublicationYear "2022" @default.
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