A new two-sphere singularity in general relativity

Details A new two-sphere singularity in general relativity A new two-sphere singularity in general relativity

2007-03-05

arxiv.org/abs/gr-qc/0703024v1

Int.J.Mod.Phys.D17:897-910,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, 3 figures

Scientific paper

10.1142/S0218271808012565

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.

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