Hawking–Page phase transition in new massive gravity

We consider Hawking–Page phase transition between the BTZ black hole with M≥0M≥0 and the thermal soliton with M=−1M=−1 in new massive gravity. By comparing the on-shell free energies, we can see that there exists a critical temperature. The thermal soliton is more probable than the black hole below the critical temperature while the black hole is more probable than the thermal soliton above the critical temperature. By consistently constructing the off-shell free energies taking into account the conical singularity, we show that there exist infinite non-equilibrium states connecting the BTZ black hole and the thermal soliton, so that they provide a picture of continuous evolution of the phase transition.