Black hole solutions in theory of ModMax-dRGT-like massive gravity

TL;DR

This paper derives and analyzes black hole solutions in a novel ModMax nonlinear electrodynamics combined with dRGT-like massive gravity, exploring their thermodynamics, stability, phase transitions, and geometric properties.

Contribution

It introduces exact black hole solutions in ModMax-dRGT-like massive gravity and studies their thermodynamic behavior and stability in both non-extended and extended phase spaces.

Findings

Thermodynamic quantities satisfy the first law and Smarr relation.

Black holes exhibit phase transitions influenced by ModMax and massive gravity parameters.

Black hole isoperimetric ratios are analyzed in this new gravity framework.

Abstract

This paper explores the properties of black holes using a new model of nonlinear electrodynamics called modified Maxwell (ModMax), in conjunction with nonlinear massive gravity known as dRGT-like massive gravity. We start by deriving the exact black hole solutions within the framework of ModMax-dRGT-like massive gravity and analyze how the parameters of both ModMax and dRGT-like massive gravity influence the characteristics of these black holes. Additionally, we calculate the thermodynamic quantities for these black holes in the non-extended phase space and investigate how the parameters of ModMax and dRGT-like massive gravity affect these quantities. We confirm that these quantities satisfy the first law of thermodynamics. We also examine local stability by analyzing heat capacity and assess how ModMax and the massive parameters influence phase transitions and physical limitation points. Next, we expand our analysis to the extended phase space, demonstrating that these thermodynamic quantities satisfy both the first law of thermodynamics and the Smarr relation in this context. Finally, we examine the isoperimetric ratio of black holes in ModMax-dRGT-like massive gravity.