Perturbation method in the assessment of radiation reaction in the capture of stars by black holes

TL;DR

This paper uses a perturbative approach to accurately identify radiation reaction effects in the radial infall of stars into black holes within Schwarzschild geometry, correcting previous misconceptions.

Contribution

It introduces a refined perturbation method that captures all relevant radiation reaction terms and renormalizes divergences, improving upon prior models.

Findings

All first-order and second-order terms identified

Divergences renormalized using special functions

Corrects previous misconceptions in the field

Abstract

This work deals with the motion of a radially falling star in Schwarzschild geometry and correctly identifies radiation reaction terms by the perturbative method. The results are: i) identification of all terms up to first order in perturbations, second in trajectory deviation, and mixed terms including lowest order radiation reaction terms; ii) renormalisation of all divergent terms by the $\zeta$ Riemann and Hurwitz functions. The work implements a method previously identified by one of the authors and corrects some current misconceptions and results.