Charged rotating BTZ black holes in noncommutative spaces and torsion gravity

TL;DR

This paper explores charged rotating BTZ black holes in noncommutative space using Chern-Simons theory, revealing that noncommutativity induces torsion and relates deformed and original Einstein equations via a coordinate transformation.

Contribution

It introduces a first-order noncommutative deformation of BTZ black holes and demonstrates the emergence of torsion within the Einstein-Cartan framework.

Findings

Noncommutativity induces nontrivial torsion.

Deformed and original Einstein equations are related by a coordinate transformation.

The deformation is captured using the Seiberg-Witten map.

Abstract

We consider charged rotating BTZ black holes in noncommutative space by use of Chern-Simons theory formulation of $2+1$ dimensional gravity. The noncommutativity between the radial and the angular variables is introduced through the Seiberg-Witten map for gauge fields, and the deformed geometry to the first order in the noncommutative parameter is derived. It is found that the deformation also induces nontrivial torsion, and the Einstein-Cartan theory appears to be a suitable framework to investigate the equations of motion. Though the deformation is indeed nontrivial, the deformed and the original Einstein equations are found to be related by a rather simple coordinate transformation.