Uniqueness of the asymptotic AdS3 geometry

TL;DR

This paper demonstrates that in (2+1) dimensions, all solutions near timelike infinity with negative cosmological constant are essentially BTZ black holes up to coordinate transformations, regardless of bulk topology or geometry.

Contribution

It proves that near timelike infinity, the asymptotic geometry in (2+1)D AdS space is uniquely characterized by BTZ metrics through coordinate deformations.

Findings

All solutions near timelike infinity are BTZ up to coordinate transformations.

The asymptotic geometry is independent of bulk topology or geometry.

The result clarifies the structure of (2+1)D AdS spacetimes near infinity.

Abstract

We explicitly show that in (2+1) dimensions the general solution of the Einstein equations with negative cosmological constant on a neigbourhood of timelike spatial infinity can be obtained from BTZ metrics by coordinate transformations corresponding geometrically to deformations of their spatial infinity surface. Thus, whatever the topology and geometry of the bulk, the metric on the timelike extremities is BTZ.