Radiation-reaction force on a particle plunging into a black hole

TL;DR

This paper computes the self-force on a scalar particle falling into a Schwarzschild black hole by numerically solving wave equations mode-by-mode and summing contributions, revealing a change from attractive to repulsive force near the horizon.

Contribution

It introduces a numerical method for calculating the self-force on a particle in black hole spacetime using mode-sum regularization in the time domain.

Findings

Radial self-force is attractive at large distances.

Force becomes repulsive near the event horizon.

Method applies mode-sum regularization to scalar fields in black hole backgrounds.

Abstract

We calculate the self force acting on a scalar particle which is falling radially into a Schwarzschild black hole. We treat the particle's self-field as a linear perturbation over the fixed Schwarzschild background. The force is calculated by numerically solving the appropriate wave equation for each mode of the field in the time domain, calculating its contribution to the self force, and summing over all modes using Ori's mode-sum regularization prescription. The radial component of the force is attractive at large distances, and becomes repulsive as the particle approaches the event horizon.