Static Ricci-flat 5-manifolds admitting the 2-sphere

Abstract

We examine, in a purely geometrical way, static Ricci-flat 5-manifolds admitting the 2-sphere and an additional hypersurface-orthogonal Killing vector. These are widely studied in the literature, from different physical approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen solutions. The 2-fold infinity of cases that result are studied by way of new coordinates (which are in most cases global) and the cases likely to be of interest in any physical approach are distinguished on the basis of the nakedness and geometrical mass of their associated singularities. It is argued that the entire class of solutions has to be considered unstable about the exceptional solutions: the black string and soliton cases. Any physical theory which admits the non-exceptional solutions as the external vacuua of a collapsing object has to accept the possibility of collapse to zero volume leaving behind the weakest possible, albeit naked, geometrical singularities at the origin.Finally, it is pointed out that these types of solutions generalize, in a straightforward way, to higher dimensions.

Generalize, in a straightforward way, to higher dimensions

References in corpus (7)

• A rotating black ring in five dimensions
• Kaluza-Klein Gravity
• Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions
• Black string instabilities in anti-de Sitter space
• Extra symmetry in the field equations in 5D with spatial spherical symmetry
• Multitemporal generalization of Schwarzschild solution
• An explicit global covering of the Schwarzschild-Tangherlini black holes

Cited by in corpus (5)

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• Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity
• SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions
• Charged seven-dimensional spacetimes with spherically symmetric extra-dimensions
• Properties of generalized Schwarzschild spacetimes with extra dimensions