No Hawking-Page phase transition in three dimensions

TL;DR

This paper examines the possibility of Hawking-Page phase transitions in three-dimensional spacetimes, concluding that such transitions do not occur, but a different second-order transition may happen between specific BTZ black holes.

Contribution

It demonstrates the absence of Hawking-Page transitions in three dimensions and identifies a potential second-order phase transition between BTZ black holes.

Findings

Hawking-Page transition does not occur in three dimensions.

A second-order transition may occur between non-rotating BTZ and massless BTZ black holes.

Hawking-Page transition is possible in even-dimensional Schwarzschild-AdS black holes.

Abstract

We investigate whether or not the Hawking-Page phase transition is possible to occur in three dimensions. Starting with the simplest class of Lanczos-Lovelock action, thermodynamic behavior of all AdS-type black holes without charge falls into two classes: Schwarzschild-AdS black holes in even dimensions and Chern-Simons black holes in odd dimensions. The former class can provide the Hawking-Page transition between Schwarzschild-AdS black holes and thermal AdS space. On the other hand, the latter class is exceptional and thus the Hawking-Page transition is hard to occur. In three dimensions, a second-order phase transition might occur between the non-rotating BTZ black hole and the massless BTZ black hole (thermal AdS space), instead of the first-order Hawking-Page transition between the non-rotating BTZ black hole and thermal AdS space.