Open Access
June 2016 On spherically symmetric solutions of the Einstein–Euler equations
Tetu Makino
Kyoto J. Math. 56(2): 243-282 (June 2016). DOI: 10.1215/21562261-3478880

Abstract

We construct spherically symmetric solutions to the Einstein–Euler equations, which give models of gaseous stars in the framework of the general theory of relativity. We assume a realistic barotropic equation of state. Equilibria of the spherically symmetric Einstein–Euler equations are given by the Tolman–Oppenheimer–Volkoff equations, and time-periodic solutions around the equilibrium of the linearized equations can be considered. Our aim is to find true solutions near these time-periodic approximations. Solutions satisfying a so-called physical boundary condition at the free boundary with the vacuum will be constructed using the Nash–Moser theorem. This work also can be considered as a touchstone in order to estimate the universality of the method which was originally developed for the nonrelativistic Euler–Poisson equations.

Citation

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Tetu Makino. "On spherically symmetric solutions of the Einstein–Euler equations." Kyoto J. Math. 56 (2) 243 - 282, June 2016. https://doi.org/10.1215/21562261-3478880

Information

Received: 14 October 2014; Revised: 6 February 2015; Accepted: 13 February 2015; Published: June 2016
First available in Project Euclid: 10 May 2016

zbMATH: 1351.35220
MathSciNet: MR3500842
Digital Object Identifier: 10.1215/21562261-3478880

Subjects:
Primary: 35L05 , 35L52 , 35L57 , 35L70
Secondary: 76L10 , 76N15 , 83C05 , 85A30

Keywords: Einstein equations , Nash–Moser theorem , spherically symmetric solutions , vacuum boundary

Rights: Copyright © 2016 Kyoto University

Vol.56 • No. 2 • June 2016
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