More Exact Thermodynamics of Nonlinear Charged AdS Black Holes in 4D Critical Gravity

TL;DR

This paper refines the thermodynamic analysis of nonlinear charged AdS black holes in 4D critical gravity, incorporating small statistical fluctuations to assess stability and thermodynamic properties.

Contribution

It provides the first detailed correction to black hole thermodynamics considering small fluctuations in this specific gravity setup.

Findings

Fluctuations induce instability in black holes.

Derived expressions for isothermal and adiabatic compressibilities.

Analyzed the impact of fluctuations on the $P-v$ diagram.

Abstract

In this paper, we investigate nonlinearly charged AdS black holes in four-dimensional critical gravity and study more exact black hole thermodynamics under the effect of small statistical fluctuations. We compute the correction to the thermodynamics of nonlinearly charged AdS black hole up to the leading order. We discuss the stability of black holes under the circumstances of fluctuation and find that fluctuation causes instability in the black holes. Moreover, both the isothermal and adiabatic compressibilities are also derived. Finally, we estimate the role of small fluctuations on the equation of states and study the $P-v$ diagram of nonlinearly charged AdS black hole.