New interpretation of the original charged BTZ black hole spacetime

Abstract

In their seminal 1992 paper, Bañados, 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 that 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, a similar construction also works for any non-linear electrodynamics in 3-dimensions. At the same time, all these spacetimes represent self-gravitating solutions of (non-linear electrodynamics generalized) force-free electrodynamics.