Spherically Symmetric Static Configurations of Uniform Density in Spacetimes with a Non-Zero Cosmological Constant

Interior solutions of Einstein’s equations with a non-zero 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 Reissner–Nordstr"om 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) Schwarzschild–de Sitter spacetime.