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arXiv · 1410.1234

On Spherically Symmetric Solutions of the Einstein-Euler Equations

Tetu Makino
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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 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 non-relativistic Euler-Poisson equations.

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Tetu Makino. 2014-10-06. On Spherically Symmetric Solutions of the Einstein-Euler Equations. https://doi.org/10.1215/21562261-3478880

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