Resonance crossing of a charged body in a magnetized Kerr background: an analogue of extreme mass ratio inspiral

TL;DR

This paper explores how a charged body in a magnetized Kerr black hole background experiences resonance crossings, serving as an electromagnetic analogue to extreme mass ratio inspirals, and assesses the accuracy of adiabatic approximations during these events.

Contribution

It introduces a model of a charged body in a magnetic Kerr background as an analogue for EMRIs and analyzes resonance crossings and the validity of adiabatic approximations in this context.

Findings

Existence of an approximate Carter-like constant in the system.

Resonance crossings can be effectively modeled using adiabatic approximations.

Adiabatic results are qualitatively consistent with instantaneous self-force evolution.

Abstract

We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficiently accuracy in EMRIs.