Global geometry of the 2+1 rotating black hole

The generic rotating BTZ black hole, obtained by identifications in AdS(3) space through a discrete subgroup of its isometry group, is investigated within a Lie theoretical context. This space is found to admit a foliation by two-dimensional leaves, orbits of a two-parameter subgroup of (SL) over tilde (2, R) and invariant under the BTZ identification subgroup. A global expression for the metric is derived, allowing a better understanding of the causal structure of the black hole. (C) 2003 Elsevier B.V. All rights reserved.