Regular black holes in three dimensions and the zero point length

TL;DR

This paper introduces a regularization method involving a zero point length to derive a non-singular, asymptotically AdS black hole solution in three dimensions, including charged and rotating cases.

Contribution

It presents a novel regularization approach to obtain exact, regular black hole solutions in three dimensions with a negative cosmological constant, extending to charged and rotating cases.

Findings

Derived a regular, non-singular black hole solution in three dimensions.

Obtained a charged BTZ black hole as a special case.

Constructed a rotating black hole solution using dimensional continuation and NJ algorithm.

Abstract

In this paper, by means of regularisation procedure via $r\to \sqrt{r^2+l_0^2}$ (where $l_0$ can play the role of zero point length), we first modify the gravitational and electromagnetic potentials in two dimensions and then we solve the Einstein field equations to end up with an exact and regular black hole solution in three dimensions with a negative cosmological constant. We show that, the black hole solution is asymptotically AdS, non-singular at the origin and, under specific conditions, it has a flat de Sitter core at the origin. As a special case, we obtain the charged Banados-Teitelboim-Zanelli (BTZ) solution. Finally, using a dimensional continuation and the NJ algorithm, we end up with a legitimate rotating black hole solution in three dimensions.