Abstract

All three-dimensional matter-free space-times with negative cosmological constant, compatible with cyclic symmetry, are identified. The only cyclic solutions are the 2 + 1 (BTZ) black hole with SO(2)×R isometry, and the self-dual Coussaert-Henneaux space-times, with isometry groups SO(2)×SO(2,1) or SO(2) ×SO(2). © 2004 The American Physical Society.