Radiation from charged particles on eccentric orbits in a dipolar magnetic field around a Schwarzschild black hole

TL;DR

This paper derives an approximate analytic expression for the electromagnetic radiation emitted by a charged particle on eccentric equatorial orbits around a Schwarzschild black hole immersed in a weak dipolar magnetic field, highlighting harmonic contributions.

Contribution

It provides the first analytic approximation for the spectral distribution of electromagnetic emission from charged particles in this specific black hole magnetic field scenario.

Findings

Analytic expression for spectral distribution derived

Identification of harmonic contributions in the emission spectrum

Approximate solution applicable to weak dipolar magnetic fields

Abstract

We obtain an approximate solution for the motion of a charged particle around a Schwarzschild black hole immersed in a weak dipolar magnetic field. We focus on eccentric bound orbits in the equatorial plane of the Schwarzschild black hole and derive an analytic expression for the spectral distribution of the electromagnetic emission from a charged particle on such an orbit. Two sets of harmonic contributions appear, with specific frequency spacing. The expression can be written in compact form, if it is truncated up to the lowest order harmonic contributions.