Classification of the static vacuum metric with Ricci-flat compactification

Details Classification of the static vacuum metric with Ricci-flat compactification Classification of the static vacuum metric with Ricci-flat compactification

Aug 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvd..34.1021y&link_type=abstract

Physical Review D (Particles and Fields), Volume 34, Issue 4, 15 August 1986, pp.1021-1024

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41

Exact Solutions, Field Theories In Dimensions Other Than Four

Scientific paper

We explicitly construct all spherically symmetric vacuum solutions of the higher-dimensional Einstein equation in which the size of Ricci-flat compact internal manifolds varies with three-dimensional distance, subject to an asymptotic condition, flat M4 times a compact manifold. Besides the usual Schwarzschild and the trivial vacuum solutions, a variety of new solutions are found, all of which contain a curvature singularity not hidden by an event horizon (naked singularity) unless the extra compact space admits an isometry.

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