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

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.