Four-dimensional anti-de Sitter black holes from a three-dimensional perspective: Full complexity

TL;DR

This paper explores the dimensional reduction of 4D anti-de Sitter black holes to a 3D perspective, revealing new solutions and analyzing their causal structure and physical properties.

Contribution

It introduces a method to derive 3D black hole solutions from 4D spacetimes with a Killing vector, providing new insights into their structure and charges.

Findings

New 3D black hole solutions from 4D reductions

Reinterpretation of charges and fields in 3D context

Analysis of causal structure of reduced solutions

Abstract

The dimensional reduction of black hole solutions in four-dimensional (4D) general relativity is performed and new 3D black hole solutions are obtained. Considering a 4D spacetime with one spacelike Killing vector, it is possible to split the Einstein-Hilbert-Maxwell action with a cosmological term in terms of 3D quantities. Definitions of quasilocal mass and charges in 3D spacetimes are reviewed. The analysis is then particularized to the toroidal charged rotating anti-de Sitter black hole. The reinterpretation of the fields and charges in terms of a three-dimensional point of view is given in each case, and the causal structure analyzed.