Phase transition of modified Horndeski gravity with new method

TL;DR

This paper introduces a modified Horndeski black hole model that exhibits phase transition behavior similar to liquid-gas systems, using a novel thermodynamic method based on the slope of temperature versus entropy.

Contribution

The study presents a new modification to Horndeski black holes enabling phase transitions and introduces a simple, effective method to analyze critical behavior in black hole thermodynamics.

Findings

Modified black holes show liquid-gas phase transition behavior.

The new method simplifies the analysis of critical points.

Some phase transition points correspond to nonphysical horizon radii.

Abstract

In this paper, we investigate the critical points of the $ P-V $ diagram and the phase transitions of the Horndenski black holes. In fact, the usual Horndeski black holes do not have $ P-V $ critical points, hence do not show any phase transitions. However, we successfully modify the Horndeski black hole solution to obtain such a phase transition behavior. This modified black holes solution is satisfied by the equation of state of liquid-gas phase transition. Also, we study the thermodynamics of our modified Horndeski black hole by applying a new method based on the equation of state that originated from the slope of temperature versus entropy. This new prescription provides us a simple powerful way to study the critical behavior and the phase transition of the black holes and concludes the novel results. The analytical interpretation of possible phase transition points leads us to set some nonphysical range on the horizon radius for the black hole.