Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory

TL;DR

This paper classifies supersymmetric, cold, and lukewarm black holes in Einstein-Maxwell theory with a cosmological constant, revealing new solutions and their properties in different cosmological backgrounds.

Contribution

It provides a comprehensive classification of cold and lukewarm black holes, including supersymmetric solutions, in Einstein-Maxwell theory with various cosmological constants.

Findings

Identified supersymmetric analogues of flat-space extreme RN black holes.

Classified lukewarm black holes at the same temperature as de Sitter background.

Discovered exotic supersymmetric solutions with infinite magnetic charge in certain limits.

Abstract

In flat space, the extreme Reissner-Nordstr\o m (RN) black hole is distinguished by its coldness (vanishing Hawking temperature) and its supersymmetry. We examine RN solutions to Einstein-Maxwell theory with a cosmological constant $\Lambda$, classifying the cold black holes and, for positive $\Lambda$, the ``lukewarm" black holes at the same temperature as the de Sitter thermal background. For negative $\Lambda$, we classify the supersymmetric solutions within the context of $N=2$ gauged supergravity. One finds supersymmetric analogues of flat-space extreme RN black holes, which for nonzero $\Lambda$ differ from the cold black holes. In addition, there is an exotic class of supersymmetric solutions which cannot be continued to flat space, since the magnetic charge becomes infinite in that limit.