No Hawking–Page phase transition in three dimensions

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.