Black Hole Perturbation Theory and Gravitational SelfForce
Abstract
Much of the success of gravitationalwave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitationalwave sources has largely focused on postNewtonian theory. However, strongfield perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extrememassratio inspirals. In this review, motivated primarily by smallmassratio binaries but not limited to them, we provide an overview of essential methods in (i) black hole perturbation theory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational selfforce theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and ReggeWheelerZerilli equations, methods of metric reconstruction, and Lorenzgauge formulations, presenting them in a new consistent and selfcontained form. Our treatment of orbital mechanics covers quasiKeplerian and actionangle descriptions of bound geodesics and accelerated orbits, osculating geodesics, nearidentity averaging transformations, multiscale expansions, and orbital resonances. Our summary of selfforce theory's foundations is brief, covering the main ideas and results of matched asymptotic expansions, local expansion methods, puncture schemes, and point particle descriptions. We conclude by combining the above methods in a multiscale expansion of the perturbative Einstein equations, leading to adiabatic and postadiabatic evolution schemes. Our presentation is intended primarily as a reference for practitioners but includes a variety of new results. In particular, we present the first complete postadiabatic waveformgeneration framework for generic (nonresonant) orbits in Kerr.
 Publication:

Handbook of Gravitational Wave Astronomy. Edited by C. Bambi
 Pub Date:
 March 2022
 DOI:
 10.1007/9789811547027_381
 arXiv:
 arXiv:2101.04592
 Bibcode:
 2022hgwa.bookE..38P
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 121 pages, 1 figure. Invited chapter for "Handbook of Gravitational Wave Astronomy" (Eds. C. Bambi, S. Katsanevas, and K. Kokkotas