Five-dimensional metrics of Petrov type 22

Abstract

We classify all five-dimensional Einstein manifolds that are static, have an SO(3) isometry group and have Petrov type 22. We use this classification to show that the localized black hole in the Randall-Sundrum scenario necessarily has Petrov type 4.

13 pages, 1 figure

References in corpus (1)

• Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1

Cited by in corpus (5)

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• Algebraic classification of higher dimensional spacetimes based on null alignment
• Six-dimensional localized black holes: numerical solutions
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
• Spinor classification of the Weyl tensor in five dimensions