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

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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 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.