Stability of 3D black hole with torsion

TL;DR

This paper investigates the supersymmetry properties of 3D black holes with torsion, revealing the number of preserved supersymmetries varies with black hole extremality and energy, and interprets ground states within the supersymmetric framework.

Contribution

It introduces an N=1+1 supersymmetric extension of 3D gravity with torsion and analyzes the supersymmetry of various black hole solutions, providing a new interpretation of ground states.

Findings

Generic black holes lack exact supersymmetries

Extremal black holes preserve one supersymmetry

Zero-energy black holes preserve two supersymmetries

Abstract

Using $N=1+1$ supersymmetric extension of the three-dimensional gravity with torsion, we show that a generic black hole has no exact supersymmetries, the extremal black hole has only one, while the zero-energy black hole has two. Combining these results with the asymptotic supersymmetry algebra, we are naturally led to interpret the zero-energy black hole as the ground state of the Ramond sector, and analogously, the anti-de Sitter solution as the ground state of the Neveau-Schwartz sector.