Eleven spherically symmetric constant density solutions with cosmological constant

TL;DR

This paper presents five new exact solutions to Einstein's field equations with a cosmological constant for static, spherically symmetric perfect fluids of constant density, including models with exterior Schwarzschild-de Sitter spacetime.

Contribution

The paper introduces five novel global solutions to Einstein's equations with a cosmological constant, expanding the set of known static, spherically symmetric models.

Findings

One solution joins the Nariai spacetime as an exterior.

Another describes a decreasing pressure model with Schwarzschild-de Sitter exterior.

Two solutions generalize the Einstein static universe.

Abstract

Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.