Nonlinear $\arcsin$-electrodynamics and asymptotic Reissner-Nordstr\"om black holes

TL;DR

This paper introduces a nonlinear electrodynamics model using an arcsin-based Lagrangian, explores its coupling with gravity, and finds asymptotic black hole solutions similar to Reissner-Nordström, with regular behavior at the origin and corrected Coulomb and black hole properties.

Contribution

The paper proposes a novel nonlinear electrodynamics model with unique invariance properties and analyzes its gravitational coupling, revealing regular black hole solutions and modifications to classical electromagnetic laws.

Findings

Derived asymptotic black hole solutions similar to Reissner-Nordström.

Demonstrated regular behavior of solutions at the origin.

Found corrections to Coulomb's law and black hole metrics.

Abstract

A model of nonlinear electrodynamics with the Lagrangian density ${\cal L} = -(1/\beta)\arcsin(\beta F_{\mu\nu}F^{\mu\nu}/4)$ is proposed. The scale invariance and the dual invariance of electromagnetic fields are broken in the model. In the limit $\beta\rightarrow 0$ one comes to Maxwell's electrodynamics and the scale and dual invariances are recovered. We investigate the effect of coupling electromagnetic fields with the gravitational field. The asymptotic black hole solution is found which is similar to the Reissner-Nordstr\"om solution. We obtain corrections to Coulomb's law and to the Reissner-Nordstr\"om solution in the model proposed. The existence of the regular asymptotic at $r\rightarrow 0$ was demonstrated. The mass of the black hole is calculated possessing the electromagnetic origin. It was shown that there are not superluminal fluctuations and principles of causality and unitarity take place.