Magnetic black holes with generalized ModMax model of nonlinear electrodynamics

TL;DR

This paper introduces a generalized ModMax nonlinear electrodynamics model coupled with gravity, analyzing magnetic black hole solutions, their properties, stability, and phase transitions, extending previous models with new regularity and thermodynamic insights.

Contribution

It develops the Generalized ModMax model of nonlinear electrodynamics coupled to gravity, deriving black hole solutions and analyzing their thermodynamic stability and phase behavior.

Findings

Black hole solutions exhibit corrections to Reissner–Nordström metric.

Some parameter choices yield regular black holes without singularities.

Black holes can be thermodynamically unstable depending on parameters.

Abstract

Recently Bandos, Lechner, Sorokin, and Townsend [Phys. Rev. D \textbf{102}, 121703 (2020)] proposed Modified Maxwell (ModMax) model of nonlinear duality-invariant conformal electrodynamics. Here, Generalized ModMax (GenModMax) model of nonlinear electrodynamics coupled to general relativity is studied. The metric and mass functions, and their asymptotic as $r\rightarrow\infty$ and $r\rightarrow 0$ of a magnetic black hole are obtained. Corrections to the Reissner--Nordstr\"{o}m solution are found and we show that for some model parameters the black hole is regular. The Hawking temperature and heat capacity of black holes are calculated and phase transitions are investigated. We demonstrate that black holes are not stable for certain model parameters.