Phase transition of black holes in Brans--Dicke Born--Infeld gravity through geometrical thermodynamics

TL;DR

This paper investigates phase transitions of Brans--Dicke Born--Infeld black holes using geometrical thermodynamics, comparing traditional and new methods to identify phase transition points and bound points.

Contribution

It introduces and compares a new geometrical thermodynamics method that accurately locates phase transitions and bound points in black hole thermodynamics.

Findings

New method's Ricci scalar diverges at phase transitions and bound points.

Bound points can be distinguished from phase transitions by the sign of the Ricci scalar.

Comparison shows the new method improves identification of thermodynamic features.

Abstract

Using the geometrical thermodynamic approach, we study phase transition of Brans--Dicke Born--Infeld black holes. We apply introduced methods and describe their shortcomings. We also use the recently proposed new method and compare its results with those of canonical ensemble. By considering the new method, we find that its Ricci scalar diverges in the places of phase transition and bound points. We also show that the bound point can be distinguished from the phase transition points through the sign of thermodynamical Ricci scalar around its divergencies.