Self-force and radiation reaction in general relativity

TL;DR

This review discusses the theory and recent advances in gravitational self-force calculations, crucial for modeling binary black hole inspirals in extreme mass ratio scenarios, bridging theory, numerics, and astrophysical applications.

Contribution

It provides a comprehensive overview of the formal derivation, numerical methods, and astrophysical relevance of gravitational self-force in curved spacetime, connecting different approaches to the two-body problem.

Findings

Progress in numerically calculating the self-force effects.

Enhanced understanding of self-force impact on inspiral dynamics.

Integration of self-force results with other two-body problem methods.

Abstract

[Abridged] This review surveys the theory of gravitational self-force in curved spacetime and its application to the gravitational two-body problem in the extreme-mass-ratio regime. We first lay the relevant formal foundation, describing the rigorous derivation of the equation of self-forced motion using matched asymptotic expansions and other ideas. We then review the progress that has been achieved in numerically calculating the self-force and its physical effects in the astrophysical scenario of a compact object inspiralling into a (rotating) massive black hole. We highlight the way in which, nowadays, self-force calculations make a fruitful contact with other approaches to the two-body problem and help inform an accurate universal model of binary black hole inspirals, valid across all mass ratios. We conclude with a summary of the state of the art, open problems and prospects. Our review is aimed at non-specialist readers and is for the most part self-contained and non-technical; only elementary-level acquaintance with General Relativity is assumed. Where useful, we draw on analogies with familiar concepts from Newtonian gravity or classical electrodynamics.