A new two-sphere singularity in general relativity

TL;DR

This paper investigates a unique spherically symmetric solution in general relativity, revealing a novel two-sphere singularity in the Florides solution, and shows how a negative cosmological constant can eliminate this singularity.

Contribution

It identifies a previously unreported two-sphere singularity in the Florides solution and explores how a negative cosmological constant removes this singularity.

Findings

Discovery of a new two-sphere singularity in the Florides solution.

The singularity involves divergence of curvature invariants and tangential pressure.

A negative cosmological constant (anti-de Sitter) removes the singularity.

Abstract

The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior Schwarzschild solution. The specific case of a constant energy density has been interpreted as the field inside an Einstein cluster. In this work, we are interested in analyzing the geometry throughout the permitted range of the radial coordinate without matching it to the Schwarzschild exterior spacetime at some constant radius hypersurface. We find an interesting picture, namely, the solution represents a three-sphere, whose equatorial two-sphere is singular, in the sense that the curvature invariants and the tangential pressure diverge. As far as we know, such singularities have not been discussed before. In the presence of a large negative cosmological constant (anti-de Sitter) the singularity is removed.