Conformal use of retarded Green's functions for the Maxwell field in de Sitter space

TL;DR

This paper introduces a new method for calculating electromagnetic fields in de Sitter space using conformal invariance and Green's functions, simplifying classical electromagnetic problems in curved spacetime.

Contribution

It presents a novel propagation formula for Maxwell fields in de Sitter space that leverages conformal invariance and Green's functions of Minkowski space.

Findings

Simplifies calculations of electromagnetic fields in de Sitter space.

Successfully applied to a classical two-charge problem in de Sitter space.

Provides a practical tool for classical field analysis in curved spacetime.

Abstract

We propose a new propagation formula for the Maxwell field in de Sitter space which exploit the conformal invariance of this field together with a conformal gauge condition. This formula allows to determine the classical electromagnetic field in the de Sitter space from given currents and initial data. It only uses the Green's function of the massless Minkowskian scalar field. This leads to drastic simplifications in practical calculations. We apply this formula to the classical problem of the two charges of opposite signs at rest at the North and South Poles of the de Sitter space.