On spherically symmetric solutions of the Einstein-Euler-de Sitter equations

TL;DR

This paper constructs spherically symmetric solutions to the Einstein-Euler-de Sitter equations with a positive cosmological constant, analyzing equilibria and solutions near linearized states, extending previous work without cosmological constants.

Contribution

It generalizes previous models by including a positive cosmological constant and constructs solutions near equilibrium states for the Einstein-Euler-de Sitter equations.

Findings

Solutions near time periodic linearized states are constructed.

The Cauchy problem around equilibrium is solvable.

Equilibria are characterized by the Tolman-Oppenheimer-Volkoff-de Sitter equation.

Abstract

We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de Sitter equations. We assume a realistic barotropic equation of state. Equilibria of the spherically symmetric Einstein-Euler-de Sitter equations are given by the Tolman-Oppenheimer-Volkoff-de Sitter equation. We can construct solutions near time periodic linearized solutions around the equilibrium. The Cauchy problem around the equilibrium can be solved. This work can be considered as a trial of the generalization of the previous work on the problem without cosmological constants.