Asymptotic Reissner-Nordstr\"om solution within nonlinear electrodynamics

TL;DR

This paper explores how nonlinear electrodynamics modifies Reissner-Nordström black hole solutions, analyzing their asymptotic behavior, thermodynamics, and stability, revealing corrections to classical laws and phase transition points.

Contribution

It provides new asymptotic solutions for charged black holes in nonlinear electrodynamics and studies their thermodynamic stability and phase transitions.

Findings

Corrections to Reissner-Nordström solution at large distances

Identification of a critical mass for stability

Existence of a second-order phase transition

Abstract

A model of nonlinear electrodynamics coupled with the gravitational field is studied. We obtain the asymptotic black hole solutions at $r\rightarrow 0$ and $r\rightarrow \infty$. The asymptotic at $r\rightarrow 0$ is shown, and we find corrections to the Reissner-Nordstr\"om solution and Coulomb's law at $r\rightarrow\infty$. The mass of the black hole is evaluated having the electromagnetic origin. We investigate the thermodynamics of charged black holes and their thermal stability. The critical point corresponding to the second-order phase transition (where heat capacity diverges) is found. If the mass of the black hole is greater than the critical mass, the black hole becomes unstable.