Effects of energy dependent spacetime on geometrical thermodynamics and heat engine of black holes: gravity's rainbow

TL;DR

This paper explores how gravity's rainbow influences the thermodynamics, phase transitions, and heat engine efficiency of charged topological black holes, revealing parameter-dependent behaviors and stability conditions.

Contribution

It introduces new black hole solutions in gravity's rainbow, analyzes their thermodynamics and phase transitions, and examines the impact on heat engine efficiency.

Findings

Black hole solutions can have two horizons, one horizon, or no horizon depending on parameters.

Thermodynamical analysis shows stability regions and phase transition points.

Heat engine efficiency is affected by topological and rainbow parameters.

Abstract

Inspired by applications of gravity's rainbow in UV completion of general relativity, we investigate charged topological black holes in gravity's rainbow and show that depending on the values of different parameters, these solutions may encounter with black hole solutions with two horizons, extreme black hole (one horizon) or naked singularity (without horizon). First, we obtain black hole solutions, calculate thermodynamical quantities of the system and check the first law of thermodynamics. Then, we study the thermodynamical behavior of the system including thermal stability and phase transitions. In addition, we employ geometrical thermodynamics to probe phase transition points and limits on having physical solutions. Finally, we obtain heat engines corresponding to these black holes. The goal is to see how black holes' parameters such as topological factor and rainbow functions would affect efficiency of the heat engines.