New interpretation of the original charged BTZ black hole spacetime

TL;DR

This paper reinterprets the original charged BTZ black hole as a solution within the Deshpande--Lunin theory, extending it to non-linear electrodynamics and force-free electrodynamics in three dimensions.

Contribution

It provides a new interpretation of the charged BTZ black hole as a solution of the Deshpande--Lunin theory, including non-linear electrodynamics and force-free electrodynamics.

Findings

Reinterpretation of the charged BTZ solution within Deshpande--Lunin theory.

Extension to non-linear electrodynamics in 3D.

Existence of self-gravitating solutions in force-free electrodynamics.

Abstract

In their seminal 1992 paper, Ba\~{n}ados, Teitelboim and Zanelli (BTZ) proposed a simple charged generalization of what is now known as the spinning BTZ black hole, the proposal being that a rotating metric can be supported by a `static vector' potential. While with such an ansatz the Einstein equations are satisfied, and the corresponding energy-momentum tensor is divergence-less, the Maxwell equations do not (due to the special degenerate form of the corresponding field strength) hold. More recently, Deshpande and Lunin have proposed a generalized `Einstein--Maxwell' system which yields analytic rotating black holes in all odd dimensions. In this paper, we show that the original charged BTZ solution can be re-interpreted as a solution of the Deshpande--Lunin theory. Moreover, as we shall explicitly illustrate on an example of regularized conformal electrodynamics, similar construction also works for any non-linear electrodynamics in 3-dimensions. At the same time, all these spacetimes represent self-gravitating solutions of (NLE generalized) force-free electrodynamics.