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

TL;DR

This paper classifies all higher-dimensional Einstein-Maxwell solutions that are products of constant curvature manifolds, including Nariai, Bertotti-Robinson, and anti-Nariai types, derived from extremal limits of black holes.

Contribution

It provides explicit higher-dimensional solutions of Einstein-Maxwell theory with specific topologies, extending known solutions to any dimension greater than three.

Findings

Explicit solutions for all D>3 dimensions.

Relations between black hole parameters and horizon radius.

New topological variants of known solutions.

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.