Three-dimensional Noncommutative Gravity

TL;DR

This paper develops a formulation of three-dimensional noncommutative gravity using Chern-Simons theory, demonstrating that 3d black holes are solutions and analyzing how background fields modify black hole charges.

Contribution

It introduces a noncommutative gravity model in 3d based on Chern-Simons theory and explores black hole solutions within this framework.

Findings

3d black holes solve noncommutative equations

Black hole charges are modified by background fields

The formulation connects noncommutative geometry with 3d gravity

Abstract

We formulate noncommutative three-dimensional (3d) gravity by making use of its connection with 3d Chern-Simons theory. In the Euclidean sector, we consider the particular example of topology $T^2 \times R$ and show that the 3d black hole solves the noncommutative equations. We then consider the black hole on a constant U(1) background and show that the black hole charges (mass and angular momentum) are modified by the presence of this background.