On a spacetime duality in 2+1 gravity

We consider (2 + 1)-dimensional gravity with a cosmological constant, and e xplore a duality that exists between spacetimes that have the de Sitter gro up SO(3, 1) as is local isometry group. In particular, the Lorentzian theor y with a positive cosmological constant is dual to the Euclidean theory wit h a negative cosmological constant. We use this duality to construct a mapp ing between apparently unrelated spacetimes. More precisely, we exhibit a r elation between the Euclidean BTZ family and some T-2-cosmological solution s, and between de Sitter point-particle spacetimes and the analytic continu ations of anti-de Sitter point particles. We discuss some possible applicat ions for black hole and anti-de Sitter thermodynamics.