Monopole and dipole layers in curved spacetimes: formalism and examples

TL;DR

This paper develops a formalism for analyzing electromagnetic layers with monopoles and dipoles in curved spacetimes, applying it to Schwarzschild disks and confirming results with the membrane paradigm.

Contribution

It introduces a comprehensive framework for electromagnetic discontinuities in curved spacetimes and applies it to specific solutions involving Schwarzschild disks.

Findings

Discontinuities of electromagnetic fields are characterized in curved spacetimes.

Electric and magnetic sources are shown to be equivalent in certain configurations.

Charge and dipole distributions on Schwarzschild disks are explicitly described.

Abstract

The discontinuities of electromagnetic test fields generated by general layers of electric and magnetic monopoles and dipoles are investigated in general curved spacetimes. The equivalence of electric currents and magnetic dipoles is discussed. The results are used to describe exact "Schwarzschild disk" solutions endowed with such sources. The resulting distributions of charge and dipole densities on the disks are corroborated using the membrane paradigm.