Black hole perturbation theory and gravitational self-force

Abstract

Much of the success of gravitational-wave astronomy rests on perturbationtheory. Historically, perturbative analysis of gravitational-wave sources has largelyfocused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger ofa binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio binaries but not limitedto them, we provide an overview of essential methods in (i) black hole perturbationtheory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational self-force theory. Our treatment of black hole perturbation theory covers most common methods,including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metricreconstruction, and Lorenz-gauge formulations, casting them in a unified notation.Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identityaveraging transformations, multiscale expansions, and orbital resonances. Our summary of self-force theory’s foundations is brief, covering the main ideas and resultsof matched asymptotic expansions, local expansion methods, puncture schemes,and point particle descriptions. We conclude by combining the above methods ina multiscale expansion of the perturbative Einstein equations, leading to adiabaticand post-adiabatic evolution and waveform-generation schemes. Our presentationincludes some new results but is intended primarily as a reference for practitioners.

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Identifiers

ORCID for Adam Pound: orcid.org/0000-0001-9446-0638

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