On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box

TL;DR

This paper investigates phase transitions between black holes and hairy black holes in asymptotically flat spacetime with a box, revealing effects of scalar mass and similarities to holographic transitions.

Contribution

It introduces a model of black hole/hairy black hole transitions with nonzero scalar mass and demonstrates the second order nature of these transitions, drawing parallels to holographic theories.

Findings

Negative scalar mass facilitates phase transitions.

The order parameter follows a square root relation near criticality.

Transitions resemble holographic black hole phase transitions.

Abstract

We study the asymptotically flat quasi-local black hole/hairy black hole model with nonzero mass of the scalar filed. We disclose effects of the scalar mass on transitions in a grand canonical ensemble with condensation behaviors of a parameter $\psi_{2}$, which is similar to approaches in holographic theories. We find that more negative scalar mass makes the phase transition easier to happen. We also obtain an analytical relation $\psi_{2}\varpropto(T_{c}-T)^{1/2}$ around the critical phase transition points implying a second order phase transition. Besides the parameter $\psi_{2}$, we show that metric solutions can be used to disclose properties of transitions. In this work, we observe that phase transitions in a box are strikingly similar to holographic transitions in the AdS gravity and the similarity provides insights into holographic theories.