Electromagnetic Fields Simulating a Rotating Sphere and its Exterior

TL;DR

This paper introduces electromagnetic field solutions in vacuum that rotate globally around an axis, exhibit circular patterns on a sphere, and can be interpreted within plasma and magnetohydrodynamics models, with potential astronomical applications.

Contribution

It presents a novel class of electromagnetic fields satisfying Maxwell's equations with unique rotational and structural properties, extending to plasma and magnetohydrodynamics contexts.

Findings

Fields form circular patterns on the sphere surface.

Solutions can be constructed using eigenfunctions of the vector Laplace operator.

Applications in astronomy are discussed.

Abstract

Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically satisfy the set of Maxwell's equations, but enjoy further properties that allow them to be suitably interpreted as solutions of a plasma model that combines electrodynamics with the Euler's equation for fluids. Connection with magnetohydrodynamics can also be established. The fields are extended with continuity outside the sphere in a very peculiar manner. In order to avoid peripheral velocities of arbitrary magnitude, as it may happen for a rigid rotating body, they are organized to form successive encapsulated shells, with substructures recalling successive ball-bearing assemblies. A recipe for the construction of these solutions is provided by playing with the eigenfunctions of the vector Laplace operator. Some applications relative to astronomy are finally discussed.