Thermodynamic stability of warped [formula omitted] black holes

Danny Birmingham,Susan Mokhtari

doi:10.1016/j.physletb.2011.01.032

Danny Birmingham, Susan Mokhtari

Open Access

https://doi.org/10.1016/j.physletb.2011.01.032

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Abstract

We study the thermodynamic stability of warped black holes in three-dimensional topologically massive gravity. The spacelike stretched black hole is parametrized by its mass and angular momentum. We determine the local and global stability properties in the canonical and grand canonical ensembles. The presence of a Hawking–Page type transition is established, and the critical temperature is determined. The thermodynamic metric of Ruppeiner is computed, and the curvature is shown to diverge in the extremal limit. The consequences of these results for the classical stability properties of warped black holes are discussed within the context of the correlated stability conjecture.

Highlights

Lower-dimensional models of gravity have provided a fruitful arena for exploring various aspects of black holes
The BTZ black hole provides a useful example of a black hole in this theory, and the classical stability against linear perturbations was established in [7]
Our primary concern here is to study the so-called spacelike stretched black hole. This black hole is obtained as a discrete quotient of a warped version of AdS3, and the geometry is parametrized by its mass, angular momentum, and a warp factor

Summary

Introduction

Lower-dimensional models of gravity have provided a fruitful arena for exploring various aspects of black holes. The presence of the BTZ black hole [1] as a solution to the Einstein field equations has led to a wealth of important results on the conformal properties of gravity. In [8]-[10], a novel class of black hole solutions to TMG was obtained These have the attractive feature that they are non-Einstein spaces, and they probe more details of the field equations of TMG. Our primary concern here is to study the so-called spacelike stretched black hole This black hole is obtained as a discrete quotient of a warped version of AdS3, and the geometry is parametrized by its mass, angular momentum, and a warp factor. We determine the local and global thermodynamic stability properties of the warped black hole in both the grand canonical and canonical ensembles. We record the local and global stability results for the BTZ black hole and show that it obeys the correlated stability conjecture

Warped Black Holes

Local and Global Thermodynamic Stability

The Correlated Stability Conjecture

Conclusions