Nonlinear Problems Inspired by the Born--Infeld Theory of Electrodynamics

TL;DR

This paper explores how Born--Infeld nonlinear electrodynamics can address fundamental physics problems such as magnetic monopoles, black hole singularities, and cosmic fluid equations, offering new theoretical insights.

Contribution

It demonstrates the application of Born--Infeld theory to fundamental issues in physics and discusses related nonlinear differential equations.

Findings

Electromagnetic asymmetry can exclude magnetic monopoles.

Finite electromagnetic energy can resolve black hole singularities.

Provides interpretation of cosmic fluid equations via k-essence cosmology.

Abstract

It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude magnetic monopoles, achieving finite electromagnetic energy to relegate curvature singularities of charged black holes, and providing theoretical interpretation of equations of state of cosmic fluids via k-essence cosmology. Also discussed are some nonlinear differential equation problems.