Spherically Symmetric Static Configurations of Uniform Density in Spacetimes with a NonZero Cosmological Constant
Abstract
Interior solutions of Einstein's equations with a nonzero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative values of the cosmological constant. Limits on the outer radius of the interior solutions are established. It is shown that, contrary to the cases of the limits on the interior Schwarzschild and ReissnerNordström solutions with a zero cosmological constant, these limits do not fully coincide with the conditions of embeddability of the optical reference geometry associated with the exterior (vacuum) Schwarzschildde Sitter spacetime.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 DOI:
 10.48550/arXiv.0803.2530
 arXiv:
 arXiv:0803.2530
 Bibcode:
 2008arXiv0803.2530S
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 11 pages