GAUGE FORMULATION OF THE SPINNING BLACK-HOLE IN (2+1)-DIMENSIONAL ANTI-DE SITTER SPACE

We compute the group element of SO(2,2) associated with the spinning black hole found by Banados, 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 Poincare limit as special cases.