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Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions

Vitor Cardoso·Oscar J. C. Dias·Jose' P. S. Lemos
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Abstract

We find all the higher dimensional solutions of the Einstein-Maxwell theory that are the topological product of two manifolds of constant curvature. These solutions include the higher dimensional Nariai, Bertotti-Robinson and anti-Nariai solutions, and the anti-de Sitter Bertotti-Robinson solutions with toroidal and hyperbolic topology (Plebanski-Hacyan solutions). We give explicit results for any dimension D>3. These solutions are generated from the appropriate extremal limits of the higher dimensional near-extreme black holes in a de Sitter, and anti-de Sitter backgrounds. Thus, we also find the mass and the charge parameters of the higher dimensional extreme black holes as a function of the radius of the degenerate horizon.

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Vitor Cardoso, Oscar J. C. Dias, Jose' P. S. Lemos. 2004-04-28. Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions. https://doi.org/10.1103/physrevd.70.024002

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