From accelerating and Poincar\'e coordinates to black holes in spacelike warped AdS$_3$, and back

TL;DR

This paper explores the geometry and causal structure of black holes in spacelike warped AdS$_3$, analyzing their coordinate systems, maximal extensions, and phase space limits to deepen understanding of their spacetime properties.

Contribution

It provides a detailed analysis of black hole quotients in warped AdS$_3$, including coordinate descriptions, causal diagrams, and phase space limits, connecting different spacetime solutions.

Findings

Derived maximal analytic extensions and causal diagrams of warped AdS$_3$ black holes.

Identified spacetime limits leading to self-dual solutions and warped AdS with periodic time.

Clarified the relationship between coordinate systems and black hole phases in warped AdS$_3$.

Abstract

We first review spacelike stretched warped AdS$_3$ and we describe its black hole quotients by using accelerating and Poincar\'e coordinates. We then describe the maximal analytic extension of the black holes and present their causal diagrams. Finally, we calculate spacetime limits of the black hole phase space $(T_R,T_L)$. This is done by requiring that the identification vector $\partial_\theta$ has a finite non-zero limit. The limits we obtain are the self-dual solution in accelerating or Poincar\'e coordinates, depending respectively on whether the limiting spacetimes are non-extremal or extremal, and warped AdS with a periodic proper time identification.