2+1 dimensional charged black hole with (anti-)self dual Maxwell fields

TL;DR

This paper presents exact solutions for charged BTZ black holes in 2+1 dimensions with (anti-)self dual Maxwell fields, addressing angular momentum divergences and regularization methods.

Contribution

It introduces exact charged black hole solutions under (anti-)self dual conditions and discusses regularization of angular momentum in these spacetimes.

Findings

Logarithmic divergence in angular momentum at infinity.

Regularization method involving boundary contributions.

Alternative coordinate choice yields finite angular momentum.

Abstract

We discuss the exact electrically charged BTZ black hole solutions to the Einstein-Maxwell equations with a negative cosmological constant in 2+1 spacetime dimensions assuming a (anti-)self dual condition between the electromagnetic fields. In a coordinate condition there appears a logarithmic divergence in the angular momentum at spatial infinity. We show how it is to be regularized by taking the contribution from the boundary into account. We show another coordinate condition which leads to a finite angular momentum though it brings about a peculiar spacetime topology.