The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole

TL;DR

This paper explores the thermodynamics of McVittie spacetime, revealing a Hawking-Page-like phase transition from FRW universe to black hole, with work density acting as pressure and a constructed thermodynamic equation of state.

Contribution

It formulates the first law of thermodynamics for McVittie black holes and demonstrates a Hawking-Page-like phase transition in this context.

Findings

Hawking-Page-like phase transition is possible for P>0.

Work density acts as thermodynamic pressure.

Thermodynamic equation of state for McVittie black hole is constructed.

Abstract

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 $P>0$.