On a spacetime duality in 2+1 gravity

TL;DR

This paper explores a duality in 2+1 gravity linking Lorentzian and Euclidean space-times with different cosmological constants, enabling mappings between various solutions and potential applications in black hole and AdS thermodynamics.

Contribution

It introduces a duality between space-times with different signatures and cosmological constants, providing a new way to relate and analyze diverse 2+1 gravity solutions.

Findings

Mapped Euclidean BTZ solutions to $T^2$-cosmologies

Related De Sitter point particles to Anti-De Sitter solutions

Discussed implications for black hole and AdS thermodynamics

Abstract

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.