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Black Hole Perturbation Theory and Gravitational Self-Force

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Handbook of Gravitational Wave Astronomy

Abstract

Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio 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 self-force theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metric reconstruction, and Lorenz-gauge formulations, presenting them in a new consistent and self-contained form. Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identity averaging transformations, multiscale expansions, and orbital resonances. Our summary of self-force 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 post-adiabatic 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 post-adiabatic waveform-generation framework for generic (nonresonant) orbits in Kerr.

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The acknowledgement of a Royal Society University Research Fellowship was a funding acknowledgement. Please reinstate it.

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  1. School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton, UK

    Adam Pound

  2. School of Mathematics and Statistics, University College Dublin, Dublin, Ireland

    Barry Wardell

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  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Université Paris Denis Diderot, Paris, France

    Stavros Katsanevas

  3. Institute for Astronomy and Astrophysics, Eberhard Karls University of Tübingen, Tübingen, Germany

    Konstantinos D. Kokkotas

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  1. Department of Physics, University of Texas at Austin, Austin, United States

    Pablo Laguna

  2. School of Physics, University of Texas at Austin, Austin, United States

    Deirdre Shoemaker

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Pound, A., Wardell, B. (2021). Black Hole Perturbation Theory and Gravitational Self-Force. In: Bambi, C., Katsanevas, S., Kokkotas, K.D. (eds) Handbook of Gravitational Wave Astronomy. Springer, Singapore. https://doi.org/10.1007/978-981-15-4702-7_38-1

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