On Spherically Symmetric Solutions of the Einstein-Euler Equations

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.

Cited by in corpus (9)

• Turning point principle for relativistic stars
• Stability and instability of self-gravitating relativistic matter distributions
• Recent developments in mathematical aspects of relativistic fluids
• The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion
• On the asymptotic behavior of static perfect fluids
• An Application of the Nash-Moser Theorem to the Vacuum Boundary Problem of Gaseous Stars
• Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system
• On slowly rotating axisymmetric solutions of the Einstein-Euler equations
• On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary