Maxwell equations in Duffin - Kemmer tetrad form, spherical waves in Riemann space S_3

TL;DR

This paper extends Maxwell equations in Duffin-Kemmer tetrad form to arbitrary Riemannian space-times, solves them exactly in a static cosmological model, and finds a discrete electromagnetic mode spectrum influenced by space curvature.

Contribution

It introduces a novel extension of Maxwell equations in Duffin-Kemmer form to arbitrary pseudo-Riemannian spaces and provides exact solutions in a curved cosmological background.

Findings

Exact solutions for Maxwell equations in Riemann space S_3

Discrete electromagnetic mode spectrum depending on curvature

Constructed 4-potentials for spherical electromagnetic waves

Abstract

The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations are solved exactly on the background of simplest static cosmological model, space of constant curvature of Riemann parameterized by spherical coordinates. Separation of variables is realized in the basis of Schr\"odinger- Pauli type, description of angular dependence in electromagnetic filed functions is given in terms of Wigner D-functions. A discrete frequency spectrum for electromagnetic modes depending on the curvature radius of space and three discrete parameters is found. 4-potentials for spherical electro- magnetic waves of magnetic and electric type have been constructed.