Supersymmetry of Anti-de Sitter Black Holes

TL;DR

This paper investigates the supersymmetry properties of various four-dimensional anti-de Sitter black holes, revealing that horizon topology influences whether rotation is necessary for supersymmetry, with unique nonrotating solutions for higher genus horizons.

Contribution

It provides a comprehensive analysis of supersymmetry in AdS black holes with different topologies, including new nonrotating solutions for higher genus horizons.

Findings

Nonrotating supersymmetric solutions exist for higher genus horizons.

Rotation is required for supersymmetry in spherical, toroidal, or cylindrical horizons.

Explicit Killing spinors are constructed for nonrotating configurations.

Abstract

We examine supersymmetry of four-dimensional asymptotically anti-de Sitter (AdS) dyonic black holes in the context of gauged N=2 supergravity. Our calculations concentrate on black holes with unusual topology and their rotating generalizations, but we also reconsider the spherical rotating dyonic Kerr-Newman-AdS black hole, whose supersymmetry properties have previously been investigated by Kosteleck\'{y} and Perry within another approach. We find that in the case of spherical, toroidal or cylindrical event horizon topology, the black holes must rotate in order to preserve some supersymmetry; the non-rotating supersymmetric configurations representing naked singularities. However, we show that this is no more true for black holes whose event horizons are Riemann surfaces of genus $g>1$, where we find a nonrotating extremal solitonic black hole carrying magnetic charge and permitting one Killing spinor. For the nonrotating supersymmetric configurations of various topologies, all Killing spinors are explicitly constructed.