Phase transitions for the Lifshitz black holes

TL;DR

This paper investigates the potential for phase transitions between Lifshitz black holes and other configurations, concluding that such transitions are unlikely due to differing asymptotic behaviors.

Contribution

It provides a detailed analysis of phase transition possibilities involving Lifshitz black holes, emphasizing the importance of asymptotic structure for such transitions.

Findings

Phase transition between Lifshitz soliton and Lifshitz black hole unlikely in three dimensions.

Phase transition between Lifshitz and BTZ black holes unlikely due to different asymptotes.

No phase transition expected between Lifshitz and black branes in four dimensions.

Abstract

We study possibility of phase transitions between Lifshitz black holes and other configurations by using free energies explicitly. A phase transition between Lifshitz soliton and Lifshitz black hole might not occur in three dimensions. We find that a phase transition between Lifshitz and BTZ black holes unlikely occurs because they have different asymptotes. Similarly, we point out that any phase transition between Lifshitz and black branes unlikely occurs in four dimensions since they have different asymptotes. This is consistent with a necessary condition for taking a phase transition in the gravitational system, which requires the same asymptote.