Abstract
We consider (2 + 1)-dimensional gravity with a cosmological constant, and explore a duality that exists between spacetimes that have the de Sitter group SO(3,1) as its local isometry group. In particular, the Lorentzian theory with a positive cosmological constant is dual to the Euclidean theory with a negative cosmological constant. We use this duality to construct a mapping between apparently unrelated spacetimes. More precisely, we exhibit a relation between the Euclidean BTZ family and some T 2-cosmological solutions, and between de Sitter point-particle spacetimes and the analytic continuations of anti-de Sitter point particles. We discuss some possible applications for black hole and anti-de Sitter thermodynamics.
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