Orbital widening due to radiation reaction around a magnetized black hole

TL;DR

This paper investigates how radiation reaction causes the orbital radius of a charged particle around a magnetized black hole to widen, highlighting conditions for this effect and its potential astrophysical relevance.

Contribution

It demonstrates that orbital widening due to radiation reaction is independent of magnetic field configuration and occurs only when the Lorentz force acts outward, with analysis of specific magnetic field scenarios.

Findings

Orbital widening occurs only when $q L B > 0$.

Widening is accompanied by large quasi-harmonic oscillations.

Effect is potentially relevant near stellar mass black holes.

Abstract

Radiation reaction acting on a charged particle moving at a stable circular orbit of a magnetized black hole can lead to the shift of the orbital radius outwards from the black hole. The effect causes increase of the energy and angular momentum of the particle measured by an observer at rest at infinity. In this note we show that "widening" of such orbits is independent of the field configuration, however, it appears only in the cases with the external Lorentz force acting outwards from the black hole. This condition corresponds to $q L B > 0$, where $q$ and $L$ are the charge and angular momentum of the particle and $B$ is intensity of the external magnetic field. As examples of the orbital widening we consider two scenarios with an external homogeneous magnetic field and a magnetic dipole field generated by a current loop around a Schwarzschild black hole. We show that the orbital widening is accompanied by quasi-harmonic oscillations of the particle which are considerably large in the magnetic dipole fields. We also estimate the timescales of orbital widening from which it follows that the effect can be relevant in the vicinity of stellar mass black holes.