Spherical and planar three-dimensional anti-de Sitter black holes

TL;DR

This paper constructs new three-dimensional anti-de Sitter black hole solutions with spherical and planar horizons using dimensional reduction techniques, extending known solutions and introducing rotating variants.

Contribution

It introduces new 3D static and rotating black hole solutions with diverse horizon topologies derived from a specific Einstein-Maxwell-Dilaton model.

Findings

New 3D black hole solutions with spherical and planar horizons.

Existence of rotating 3D black holes derived from static solutions.

Analogies to 4D Reissner-Nordström-AdS black holes.

Abstract

The technique of dimensional reduction was used in a recent paper (Zanchin et al, Phys. Rev. D66, 064022,(2002)) where a three-dimensional (3D) Einstein-Maxwell-Dilaton theory was built from the usual four-dimensional (4D) Einstein-Maxwell-Hilbert action for general relativity. Starting from a class of 4D toroidal black holes in asymptotically anti-de Sitter (AdS) spacetimes several 3D black holes were obtained and studied in such a context. In the present work we choose a particular case of the 3D action which presents Maxwell field, dilaton field and an extra scalar field, besides gravity field and a negative cosmological constant, and obtain new 3D static black hole solutions whose horizons may have spherical or planar topology. We show that there is a 3D static spherically symmetric solution analogous to the 4D Reissner-Nordstr\"om-AdS black hole, and obtain other new 3D black holes with planar topology. From the static spherical solutions, new rotating 3D black holes are also obtained and analyzed in some detail.