# Black hole thermodynamics in Lovelock gravity's rainbow with (A)dS asymptote

## TL;DR

This paper introduces new topological black hole solutions in Lovelock gravity's rainbow with (A)dS asymptote, analyzing their thermodynamics, stability, and critical behavior in extended phase space.

## Contribution

It combines Lovelock gravity with gravity's rainbow to produce novel black hole solutions and studies their thermodynamic properties and stability.

## Key findings

- Black hole solutions satisfy the first law of thermodynamics.
- Thermal stability depends on rainbow functions and phase space parameters.
- Critical behavior and phase transitions are characterized in extended phase space.

## Abstract

In this paper, we combine Lovelock gravity with gravity's rainbow to construct Lovelock gravity's rainbow. Considering the Lovelock gravity's rainbow coupled to linear and also nonlinear electromagnetic gauge fields, we present two new classes of topological black hole solutions. We compute conserved and thermodynamic quantities of these black holes (such as temperature, entropy, electric potential, charge and mass) and show that these quantities satisfy the first law of thermodynamics. In order to study the thermal stability in canonical ensemble, we calculate the heat capacity and determinant of the Hessian matrix and show in what regions there are thermally stable phases for black holes. Also, we discuss the dependence of thermodynamic behavior and thermal stability of black holes on rainbow functions. Finally, we investigate the critical behavior of black holes in the extended phase space and study their interesting properties.