We study the 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 is unlikely to occur because they have different asymptotes. Similarly, we point out that any phase transition between Lifshitz and black branes is unlikely to occur in four dimensions since they have different asymptotes. This is consistent with the necessary condition for taking a phase transition in a gravitational system, which requires the same asymptote.
Black Hole Soliton Black Hole Solution Helmholtz Free Energy Black Brane
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We would like to thank Javier Tarrio for pointing out correctness of free energy in the Lifshitz brane. This work was supported by the 2012 Inje University research grant.