Electromagnetic sources distributed on shells in a Schwarzschild background

TL;DR

This paper investigates electromagnetic fields generated by spherical shells with smooth charge distributions in a Schwarzschild black hole background, analyzing field discontinuities and their relation to sources.

Contribution

It extends previous work by focusing on spherical shell sources with smooth charge distributions and examining field discontinuities in a Schwarzschild spacetime.

Findings

Analysis of field discontinuities related to shell sources

Characterization of electromagnetic fields from spherical shells

Insights into electromagnetic behavior near black holes

Abstract

In the Introduction we briefly recall our previous results on stationary electromagnetic fields on black-hole backgrounds and the use of spin-weighted spherical harmonics. We then discuss static electric and magnetic test fields in a Schwarzschild background using some of these results. As sources we do not consider point charges or current loops like in previous works, rather, we analyze spherical shells with smooth electric or magnetic charge distributions as well as electric or magnetic dipole distributions depending on both angular coordinates. Particular attention is paid to the discontinuities of the field, of the 4-potential, and their relation to the source.