Radiation reaction of charged particles orbiting magnetized Schwarzschild black hole

TL;DR

This paper investigates the effects of radiation reaction on charged particles orbiting a magnetized Schwarzschild black hole, analyzing stability, orbit shifts, and energy loss using covariant equations and numerical methods.

Contribution

It demonstrates the reduction of the DeWitt-Brehme equation to the Lorenz-Dirac form in vacuum metrics and compares different approaches to modeling radiation reaction in curved spacetime.

Findings

Charged particles can stabilize or spiral into the black hole depending on Lorentz force orientation.

Orbit shifts outward due to radiation reaction effects.

Energy and angular momentum losses are quantified for different orbital configurations.

Abstract

In many astrophysically relevant situations radiation reaction force acting upon a charge can not be neglected and the question arises about the location and stability of circular orbits in such regime. Motion of point charge with radiation reaction in flat spacetime is described by Lorenz-Dirac (LD) equation, while in curved spacetime -- by DeWitt-Brehme (DWB) equation containing the Ricci term and the tail term. We show that for the motion of elementary particles in vacuum metrics the DWB equation can be reduced to the covariant form of the LD equation which we use here. Generically, the LD equation is plagued by runaway solutions, so we discuss computational ways to avoid this problem in constructing numerical solutions. We also use the first iteration of the covariant LD equation which is the covariant Landau-Lifshitz equation, comparing results of these two approaches and showing smallness of the third-order Schott term in the ultrarelativistic case. We calculate the corresponding energy and angular momentum loss of a particle and study the damping of charged particle oscillations around an equilibrium radius. We find that depending on the orientation of the Lorentz force, the oscillating charged particle either spirals down to the black hole, or stabilizes the circular orbit by decaying its oscillations. The later case leads to an interesting new result of shifting of the particle orbit outwards from the black hole. We also discuss the astrophysical relevance of the presented approach and provide estimations of the main parameters of the model.