The Hawking-Page-like phase transition from FRW spacetime to McVittie black hole

In this paper, we investigate the thermodynamics especially the Hawking-Page-like phase transition of the McVittie space-time. We formulate the first law of thermodynamics for the McVittie black hole, and find that the work density W of the perfect fluid plays the role of the thermodynamic pressure, i.e. P :=- W . We also construct the thermodynamic equation of state for the McVittie black hole. Most importantly, by analysing the Gibbs free energy, we find that the Hawking-Page-like phase transition from FRW spacetime to McVittie black hole is possible in the case P > 0.