Dyonic Matter Equations, Exact Point-Source Solutions, and Charged Black Holes in Generalized Born--Infeld Theory

TL;DR

This paper derives equations for static dyonic matter in nonlinear Born--Infeld electrodynamics, finds exact solutions including black holes, and explores their implications for electromagnetic symmetry and cosmology, especially in the quadratic model.

Contribution

It introduces exact solutions for dyonic point sources in generalized Born--Infeld theory and analyzes their cosmological and black hole properties, highlighting the quadratic model's unique features.

Findings

Quadratic nonlinearity restores electromagnetic symmetry with monopoles.

Exact finite-energy dyonic solutions are obtained for specific nonlinear models.

Quadratic model supports a radiation-dominated early universe era.

Abstract

We derive the equations of motion governing static dyonic matters, described in terms of two real scalar fields, in nonlinear electrodynamics of the Born--Infeld theory type. We then obtain exact finite-energy solutions of these equations in the quadratic and logarithmic nonlinearity cases subject to dyonic point-charge sources and construct dyonically charged black holes with relegated curvature singularities. In the case of quadratic nonlinearity, which is the core model of this work, we show that dyonic solutions enable us to restore electromagnetic symmetry, which is known to be broken in non-dyonic situations by exclusion of monopoles. We further demonstrate that in the context of k-essence cosmology the nonlinear electrodynamics models possess their own distinctive signatures in light of the underlying equations of state of the cosmic fluids they represent. In this context, the quadratic and logarithmic models are shown to resolve a density-pressure inconsistency issue exhibited by the original Born--Infeld model k-essence action function as well as by all of its fractional-powered extensions. Moreover, it is shown that the quadratic model is uniquely positioned to give rise to a radiation-dominated era in the early universe among all the polynomial models and other examples considered.