Electromagnetic radiation reaction and energy extraction from black holes: The tail term cannot be ignored

TL;DR

The paper shows that in curved spacetime, especially around magnetized black holes, the tail term in the DeWitt-Brehme radiation reaction cannot be neglected. Using the Newtonian limit and a magnetized Schwarzschild background, it demonstrates that the dissipative tail component can dominate the radiation-reaction force when gravity is significant, eliminating the previously reported orbital-widening energy extraction. The authors provide analytical and numerical evidence that including the tail term yields energy loss and inspiral rather than energy gain, challenging earlier claims and underscoring the tail term as essential for consistent dynamics of radiating charges in GR. The work highlights the need to include nonlocal tail contributions in modeling EM radiation reaction in curved spacetime, with implications for understanding particle energetics near BHs and for future strong-field analyses.

Abstract

We study electromagnetic radiation reaction in curved space and the dynamics of radiating charged particles. The equation of motion for such particles is the DeWitt-Brehme equation, and it contains a particularly complicated, non-local, tail term. It has been claimed that the tail term can be neglected in certain magnetized black hole spacetimes, and that radiation reaction may then lead to energy extraction ("orbital widening") in the absence of an ergoregion. We show that such claims are incorrect, at least in the Newtonian limit: the tail term can never be neglected consistently in the relevant scenarios, and when it is included the reported energy extraction no longer occurs. Thus, previous results are called into question by our work.

Figures (1)

• Figure 1: Trajectories of a charged particle in a plus configuration orbit, with the parameters given in Table \ref{['tab:simulation']}. The red circle represents the initial orbit, with the subsequent particle motion plotted in black. Left panel -- motion without the inclusion of $\boldsymbol{F}_\text{tail}$. Right panel -- motion with the inclusion of $\boldsymbol{F}_\text{tail}$. We can see that if the tail is neglected then the particle gains energy and the orbit drifts away from the BH, as a consequence of the positive work done by $\boldsymbol{F}_{RR}$ (left). By contrast, if the tail term $\boldsymbol{F}_\text{tail}$ is included then it does enough negative work so that the particle loses energy and starts falling into the BH (right).