Phase Transitions of the BTZ Black Hole in New Massive Gravity

Abstract

We investigate thermodynamics of the BTZ black hole in new massive gravity explicitly. For m 2 l 2 > 1 / 2 with m 2 being the mass parameter of fourth-order terms and l 2 AdS 3 curvature radius, the Hawking-Page phase transition occurs between the BTZ black hole and AdS (thermal) soliton. For m 2 l 2 < 1 / 2, however, this transition unlikely occurs but a phase transition between the BTZ black hole and the massless BTZ black hole is possible to occur. We may call the latter the inverse Hawking-Page phase transition and this transition is favored in the new massive gravity.