Gauge formulation of the spinning black hole in (2+1)-dimensional anti-de Sitter space

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Abstract
We compute the group element of SO(2,2) associated with the spinning black hole found by Bañados, 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 a negative cosmological constant. Moreover, although the metric is singular on the horizons, the group element is continuous and possesses a kink there. We also consider the extremal configurations and the Poincaré limit as special cases.
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