Linear waves around static dyon solution of nonlinear electrodynamics

TL;DR

This paper investigates linear wave behavior around a static dyon solution in nonlinear electrodynamics, discovering resonance phenomena and exploring implications for gravitational interactions through energy density analysis.

Contribution

It introduces a detailed analysis of linear waves around a static dyon in nonlinear electrodynamics, including resonance effects and potential gravitational implications.

Findings

Resonance frequencies are identified numerically.

Resonance wave modes are characterized.

Energy density at infinity shows inverse radius dependence.

Abstract

Nonlinear electrodynamics model in hypercomplex form is considered. Its linearization around a solution is obtained. The appropriate problem for linear waves around static dyon solution (SDS) of Born-Infeld electrodynamics is investigated. Two types of wave scattering on SDS are considered: dissipative (with momentum transmission from plane wave to SDS) and non-dissipative (for SDS imbedded to an equilibrium wave background). Resonance phenomenon in the problem is discovered and some resonance frequencies are obtained by using a numerical method. The form of resonance wave modes are discussed. The sum of a plane wave (as the elementary component of the wave background) with one resonance mode is considered. The appropriate energy density is investigated at infinity. The averaged energy density is demonstrated to have the term proportional to inverse radius. This fact allow to consider such field configurations as the cause of gravitational interaction, taking into account the effective Riemann space effect discovered in my previous works. A behavior of the linearized solution at origin of coordinates and the problem beyond the linearization are discussed.