Gauge Formulation of the Spinning Black Hole in (2+1)-Dimensional Anti-de Sitter Space

TL;DR

This paper presents a gauge-theoretic formulation of the spinning black hole in (2+1)-dimensional anti-de Sitter space, revealing gauge invariance and continuity properties despite metric singularities.

Contribution

It introduces a gauge group element approach to describe the spinning black hole, showing the metric's gauge invariance and continuity at horizons.

Findings

The group element of SO(2,2) is computed for the black hole.

The metric is gauge invariant and satisfies Einstein's equations except at the singularity.

The group element remains continuous across horizons despite metric singularities.

Abstract

We compute the group element of SO(2,2) associated with the spinning black hole found by Ba\~nados, Teitelboim and Zanelli in (2+1)-dimensional anti-de Sitter space-time. We show that their metric is built with SO(2,2) gauge invariant quantities and satisfies Einstein's equations with negative cosmological constant everywhere except at $r=0$. Moreover, although the metric is singular on the horizons, the group element is continuous and possesses a kink there.