Exponential Modification of AdS Black Hole and Thermodynamic Behavior

TL;DR

This paper introduces an exponential modification to the AdS black hole action without matter fields, deriving an approximate solution and analyzing its thermodynamic phase transitions, which resemble Hawking-Page transitions rather than Van der Waals behavior.

Contribution

It proposes a novel exponential modification to the AdS black hole action and explores its thermodynamic properties and phase transition behavior.

Findings

Thermodynamic phase transitions of first and second types can occur.

The phase transition behavior resembles Hawking-Page transitions.

Van der Waals fluid behavior is not observed in this model.

Abstract

In this paper, we present an exponential modification for the action of an AdS black hole in the absence of a matter field. An approximated black hole solution is obtained up to the third order of perturbation coefficient. A thermodynamic investigation in canonical ensemble shows that the behavior of a Van der Waals fluid is not seen in this model. Nevertheless, the study of thermodynamic potentials and other related quantities suggests that the thermodynamic phase transitions of the first and second types can occur in this model. The forms of the phase transitions are more similar to the Hawking-Page phase transitions.