Extended phase space of Black Holes in Lovelock gravity with nonlinear electrodynamics

TL;DR

This paper explores the thermodynamics of black holes in Lovelock gravity with nonlinear electrodynamics, analyzing phase transitions and the effects of various parameters on critical behavior and thermodynamic laws.

Contribution

It extends the black hole thermodynamics framework by incorporating Lovelock gravity and nonlinear electrodynamics, modifying the first law and Smarr formula with new thermodynamic variables.

Findings

Critical values of pressure, volume, and temperature are obtained.

Phase diagrams reveal opposite effects of nonlinearity and gravity.

Universal ratio varies with nonlinearity and Lovelock parameters.

Abstract

In this paper, we consider Lovelock gravity in presence of two Born-Infeld types of nonlinear electrodynamics and study their thermodynamical behavior. We extend the phase space by considering cosmological constant as a thermodynamical pressure. We obtain critical values of pressure, volume and temperature and investigate the effects of both the Lovelock gravity and the nonlinear electrodynamics on these values. We plot $P-v$, $T-v$ and $G-T$ diagrams to study the phase transition of these thermodynamical systems. We show that power of the nonlinearity and gravity have opposite effects. We also show how considering cosmological constant, nonlinearity and Lovelock parameters as thermodynamical variables will modify Smarr formula and first law of thermodynamics. In addition, we study the behavior of universal ratio of $\frac{P_{c}v_{c}}{T_{c}}$ for different values of nonlinearity power of electrodynamics as well as the Lovelock coefficients.