Regular black holes in an asymptotically de Sitter universe

TL;DR

This paper constructs and analyzes regular black hole solutions in an asymptotically de Sitter universe, focusing on degenerate horizons, near horizon geometries, and special cases like lukewarm black holes.

Contribution

It provides explicit regular black hole solutions in de Sitter space with detailed analysis of degenerate horizons and near horizon geometries, including novel topological configurations.

Findings

Solutions include $AdS_{2}\times S^{2}$, $dS_{2}\times S^{2}$, and Plebański-Hacyan geometries.

Degenerate horizons are characterized and their near horizon limits are analyzed.

Lukewarm black hole solutions are briefly discussed.

Abstract

A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis is put on the degenerate configurations (when at least two horizons coincide) and their near horizon geometry. It is explicitly demonstrated that approximating the metric potentials in the region between the horizons by simple functions and making use of a limiting procedure one obtains the solutions constructed from maximally symmetric subspaces with different absolute values of radii. Topologically they are $AdS_{2}\times S^{2}$ for the cold black hole, $dS_{2}\times S^{2}$ when the event and cosmological horizon coincide, and the Pleba\'nski- Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyzed