Supersymmetry of the extreme rotating toroidal black hole

TL;DR

This paper investigates the supersymmetry properties of charged rotating toroidal black holes, revealing that only specific configurations, including a non-rotating charged case and an extreme uncharged rotating black hole, preserve supersymmetry.

Contribution

It identifies the conditions under which toroidal black holes preserve supersymmetry and explicitly calculates Killing spinors for the extreme uncharged case.

Findings

Non-rotating charged naked singularities are supersymmetric.

Extreme uncharged rotating black holes preserve supersymmetry.

Supersymmetry is absent in other charged rotating configurations.

Abstract

We study the supersymmetry of the charged rotating toroidal black hole solutions found by Lemos and Zanchin, and show that the only configurations that are supersymmetric are: (i) the non-rotating electrically charged naked singularities already studied by Caldarelli and Klemm, and (ii) an extreme rotating toroidal black hole with zero magnetic and electric charges. For this latter case, the extreme uncharged black hole, we calculate the Killing spinors and show that the configuration preserves the same supersymmetries as the background spacetime.