Electrostatic and Magnetostatic Solutions in a Lorentz-Violating Electrodynamics Model

TL;DR

This paper develops a Lorentz-violating electrodynamics model based on a static de Sitter metric, deriving solutions for electrostatic and magnetostatic fields, and explores the implications of Lorentz violation in electromagnetic phenomena.

Contribution

It introduces a novel Lorentz-violating electrodynamics framework using a de Sitter metric deviation and derives explicit electrostatic and magnetostatic solutions.

Findings

Electrostatic field solution for a point charge

Magnetostatic field solution for a circle current

Discussion on Lorentz violation effects in electromagnetic fields

Abstract

We propose an effective Lorentz violating electrodynamics model via static de Sitter metric which is deviated from Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we get the solutions of electrostatic field and magnetostatic field due to a point charge and a circle current respectively and discussed the implication of the effect of Lorentz violation in our electromagnetic theory.