On a spacetime duality in 2+1 gravity

Details On a spacetime duality in 2+1 gravity On a spacetime duality in 2+1 gravity

1999-06-17

arxiv.org/abs/gr-qc/9906078v2

Class.Quant.Grav. 16 (1999) 3579-3598

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, 2 figures, Revtex file

Scientific paper

10.1088/0264-9381/16/11/309

We consider 2+1 dimensional gravity with a cosmological constant, and explore a duality that exists between space-times 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 space-times. More precisely, we exhibit a relation between the Euclidean BTZ family and some $T^2$-cosmological solutions, and between De-Sitter point particle space-times and the analytic continuations of Anti-De Sitter point particles. We discuss some possible applications for BH and AdS thermodynamics.

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