Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole

TL;DR

This paper calculates the gravitational self-force on a particle plunging into a Schwarzschild black hole using a mode-sum method, improving convergence and computational efficiency through analytic approximations.

Contribution

It introduces an improved mode-sum regularization technique with enhanced convergence for self-force calculations in black hole spacetimes.

Findings

Mode-sum method effectively computes self-force.

Analytic large-ℓ approximation improves convergence.

Equivalence with ζ-function regularization confirmed.

Abstract

We compute the gravitational self-force (or ``radiation reaction'' force) acting on a particle falling radially into a Schwarzschild black hole. Our calculation is based on the ``mode-sum'' method, in which one first calculates the individual $\ell$-multipole contributions to the self-force (by numerically integrating the decoupled perturbation equations) and then regularizes the sum over modes by applying a certain analytic procedure. We demonstrate the equivalence of this method with the $\zeta-$function scheme. The convergence rate of the mode-sum series is considerably improved here (thus notably reducing computational requirements) by employing an analytic approximation at large $\ell$.