Electromagnetic radiation-reaction near black holes: orbital widening and the role of the tail

TL;DR

This paper analyzes the electromagnetic self-force on a charged particle orbiting a black hole, demonstrating that orbital widening persists even when including tail effects, with implications for astrophysical phenomena.

Contribution

The study derives analytic expressions for electromagnetic self-force components and shows that orbital widening remains significant when tail effects are included, extending previous understanding.

Findings

Orbital widening persists with tail effects included.

Tail contribution is negligible for realistic charge-to-mass ratios.

Scaling symmetry allows realistic astrophysical simulations.

Abstract

We investigate the orbital evolution of a classical charged particle around a Schwarzschild black hole immersed in an external, uniform magnetic field, taking into full account both local radiation-reaction and the nonlocal tail self-force arising in curved spacetime. Starting from the DeWitt-Brehme equation and its Landau-Lifshitz reduction, we derive analytic expressions for the conservative and dissipative components of the electromagnetic self-force in both the weak-field (Newtonian) and strong-field regimes. By implementing backward-in-time integration of the third-order DeWitt-Brehme equation alongside the second-order Landau-Lifshitz equation, we demonstrate that the so-called orbital widening effect persists even when the tail term is included, and that for astrophysically realistic charge-to-mass ratios the tail contribution to the trajectory is negligible. We further show that this widening is directly controlled by the product of the magnetic field and radiation-reaction parameters and can be captured in the Newtonian limit. Finally, we identify a scaling symmetry showing that simulations with moderate parameter values can accurately represent the dynamics in realistic astrophysical conditions, confirming that orbital widening is a robust phenomenon that can persist even in astrophysical black hole environments.