Global geometry of the 2+1 rotating black hole

TL;DR

This paper explores the global geometric structure of the rotating BTZ black hole in AdS3 space, providing a foliation and a global metric expression to clarify its causal structure.

Contribution

It introduces a Lie theoretical approach to analyze the rotating BTZ black hole, deriving a global metric and foliation that enhance understanding of its geometry and causal properties.

Findings

Identifies a foliation by two-dimensional orbits of SL(2,R)

Derives a global expression for the BTZ black hole metric

Clarifies the causal structure of the rotating black hole

Abstract

The generic rotating BTZ black hole, obtained by identifications in AdS3 space through a discrete subgroup of its isometry group, is investigated within a Lie theoretical context. This space is found to admit a foliation by two-dimensional leaves, orbits of a two-parameter subgroup of SL(2,R) and invariant under the BTZ identification subgroup. A global expression for the metric is derived, allowing a better understanding of the causal structure of the black hole.