A point mass in an isotropic universe. Existence, uniqueness and basic properties

Details A point mass in an isotropic universe. Existence, uniqueness and basic properties A point mass in an isotropic universe. Existence, uniqueness and basic properties

1998-05-12

arxiv.org/abs/gr-qc/9805041v1

Phys.Rev. D58 (1998) 064006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.58.064006

Criteria which a space-time must satisfy to represent a point mass embedded in an open Robertson--Walker (RW) universe are given. It is shown that McVittie's solution in the case $k=0$ satisfies these criteria, but does not in the case $k=-1$. Existence of a solution for the case $k=-1$ is proven and its representation in terms of an elliptic integral is given. The following properties of this and McVittie's $k=0$ solution are studied; uniqueness, behaviour at future null infinity, recovery of the RW and Schwarzschild limits, compliance with energy conditions and the occurence of singularities. Existence of solutions representing more general spherical objects embedded in a RW universe is also proven.

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