Electrodynamics in noninertial frames

TL;DR

This paper develops a covariant framework for electromagnetism in noninertial frames, especially rotating systems, deriving stationary solutions of Maxwell's equations and revisiting classical problems like Schiff's.

Contribution

It introduces a generally covariant approach to electromagnetism in noninertial frames, providing new solutions and insights into electromagnetic behavior in rotating reference systems.

Findings

Derived stationary solutions of Maxwell's equations in noninertial rotating frames.

Expressed solutions in terms of scalar functions satisfying Poisson and biharmonic equations.

Revisited and critically analyzed the classical Schiff problem.

Abstract

The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of Maxwell's electrodynamics arises in the flat Minkowski spacetime when the general coordinate transformations are restricted to a class of transformations preserving the Minkowski line element. The particular attention is paid to the analysis of the electromagnetism in the noninertial rotating reference system. For the latter case, the general stationary solution of the Maxwell equations in the absence of the electric current is constructed in terms of the two scalar functions satisfying the Poisson and the biharmonic equations with an arbitrary charge density as a matter source. The classic problem of Schiff is critically revisited.