Second-order gravitational self-force in a highly regular gauge

Upton, Samuel D.; Pound, Adam

doi:10.1103/physrevd.103.124016

Cited by 25 publications

(19 citation statements)

References 108 publications

(293 reference statements)

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“…The stress-energy tensor is then defined by the left-hand side. Through second order, it can be shown to be the stress-energy of a spinning particle in the effective metric [43,80,151,153,193]: 20…”

Section: S(n)mentioning

confidence: 99%

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Black hole perturbation theory and gravitational self-force

Pound,

Wardell

2021

Preprint

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100

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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, 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-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 and waveform-generation schemes. Our presentation includes some new results but is intended primarily as a reference for practitioners.

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Section: S(n)mentioning

confidence: 99%

“…As explained in the discussion around Eq. (193), such an approximation would accumulate large errors with time: the "small" corrections to the trajectory would grow large as the object spirals inward. The growing correction, represented by z α 1 = m α /m in Eq.…”

Section: Structure Of the Expansionmentioning

confidence: 99%

Black hole perturbation theory and gravitational self-force

Pound,

Wardell

2021

Preprint

Self Cite

100

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“…since the difference would only contribute at order ε 3 . Unlike the equations of motion (6), the stress-energy tensor (9) has been rigorously derived from the method of matched asymptotic expansions [46,50]. It holds for black holes, material bodies, and exotic compact objects.…”

Section: B Effective Metric Self-force and Self-torquementioning

confidence: 99%

Self-Force Calculations with a Spinning Secondary

Mathews,

Pound,

Wardell

2021

Preprint

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We compute the linear metric perturbation to a Schwarzschild black hole generated by a spinning compact object, specialising to circular equatorial orbits with an (anti-)aligned spin vector. We derive a two-timescale expansion of the field equations, with an attendant waveform-generation framework, that includes all effects through first post-adiabatic order, and we use the Regge-Wheeler-Zerilli formalism in the frequency domain to generate waveforms that include the complete effect of the spin on the waveform phase. We perform the calculations using expansions at fixed orbital frequency, increasing the computational efficiency and simplifying the procedure compared to previous approaches. Finally, we provide the first fully relativistic, first-principles regularisation procedure for gauge invariant self-force quantities to linear order in spin. We use this procedure to produce the first strong-field, conservative self-force calculation including the spin of the secondary -computing Detweiler's redshift invariant.

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“…The leading order self-force motion is an adiabatic inspiral. Over the longer timescale, it is necessary to consider various postadiabatic corrections currently under development [46,47]. Since we are interested in the tidal field from a nearby star or BH, another term denoting the tidal force is introduced in evolution equations ðg i;td ; G i;td Þ.…”

Section: B Tidal Resonancesmentioning

confidence: 99%