Comment on the Calculation of the Angular Momentum and Mass for the (Anti-) Self Dual Charged Spinning $BTZ$ Black Hole

TL;DR

This paper critiques a recent claim about a charged spinning BTZ black hole solution, highlighting that the derived angular momentum and mass diverge at infinity, rendering the solution unphysical.

Contribution

It clarifies that imposing a (anti-) self dual condition leads to unphysical divergences in mass and angular momentum for the charged BTZ black hole.

Findings

Angular momentum diverges at infinity.

Mass diverges at infinity.

The solution is unphysical due to these divergences.

Abstract

A recent paper [M. Kamata and T. Koikawa, Phys. Lett. {\bf B353} (1995) 196.] claimed to obtain the charged version of the $(2+1)$-dimensional spinning $BTZ$ black hole solution by assuming a (anti-) self dual condition imposed on the electric and magnetic fields. We point out that the angular momentum and mass diverge at spatial infinity and as a consequence the solution is unphysical