Black Hole Perturbation Theory and Gravitational Self-Force

Pound, Adam; Wardell, Barry

doi:10.1007/978-981-15-4702-7_38-1

Cited by 41 publications

(52 citation statements)

References 161 publications

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“…This equation expresses a remarkable simplification in the treatment of Kerr perturbations in contrast with generic backgrounds, and stands as a cornerstone of the modern black hole perturbation theory (BHPT) framework (see e.g. [77] for a recent review). In this paper, Part I, we will consider the scattering of waves of helicity h = 0, 1/2, 1 and extend previous BHPT results [9,[78][79][80][81][82][83] to all orders in spin, by introducing novel Feynman diagrammatic rules for our QFT higher-spin amplitudes.…”

Section: Jhep03(2023)136mentioning

confidence: 99%

Scattering in black hole backgrounds and higher-spin amplitudes. Part I

Bautista

Guevara

Kavanagh

et al. 2023

J. High Energ. Phys.

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The scattering of massless waves of helicity $$ \mid h\mid =0,\frac{1}{2},1 $$ ∣ h ∣ = 0 , 1 2 , 1 in Schwarzschild and Kerr backgrounds is revisited in the long-wavelength regime. Using a novel description of such backgrounds in terms of gravitating massive particles, we compute classical wave scattering in terms of 2 → 2 QFT amplitudes in flat space, to all orders in spin. The results are Newman-Penrose amplitudes which are in direct correspondence with solutions of the Regge-Wheeler/Teukolsky equation. By introducing a precise prescription for the point-particle limit, in Part I of this work we show how both agree for h = 0 at finite values of the scattering angle and arbitrary spin orientation.Associated classical observables such as the scattering cross sections, wave polarizations and time delay are studied at all orders in spin. The effect of the spin of the black hole on the polarization and helicity of the waves is found in agreement with previous analysis at linear order in spin. In the particular limit of small scattering angle, we argue that wave scattering admits a universal, point-particle description determined by the eikonal approximation. We show how our results recover the scattering eikonal phase with spin up to second post-Minkowskian order, and match it to the effective action of null geodesics in a Kerr background. Using this correspondence we derive classical observables such as polar and equatorial scattering angles.This study serves as a preceding analysis to Part II, where the Gravitational Wave (h = 2) case will be studied in detail.

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Section: Jhep03(2023)136mentioning

confidence: 99%

Scattering in black hole backgrounds and higher-spin amplitudes. Part I

Bautista

Guevara

Kavanagh

et al. 2023

J. High Energ. Phys.

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“…lmω are the solutions of homogeneous radial Teukolsky equation satisfying ingoing (upgoing) boundary conditions (see, e.g., Eqs. (92) in [4]). The functions A i are Thanks to the flux-balance laws, the rate of loss in E and L z is equal to the GW fluxes of energy and angular momentum to infinity and through the horizon.…”

Section: Gravitational Wave Fluxes and Generic Adiabatic Inspiralmentioning

confidence: 98%

“…The extreme difference in the mass ratio between the secondary and the primary allows us to treat the influence of the secondary as a perturbation to the primary's background spacetime [3,4]. This background is expected to be sufficient enough described by a Kerr spacetime.…”

Section: Introductionmentioning

confidence: 99%

Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime

Kerachian¹,

Polcar²,

Skoupý³

et al. 2023

Preprint

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We introduce an action-angle formalism for bounded geodesic motion in Kerr black hole spacetime using canonical perturbation theory. Namely, we employ a Lie series technique to produce a series of canonical transformations on a Hamiltonian function describing geodesic motion in Kerr background written in Boyer-Lindquist coordinates to a Hamiltonian system written in action-angle variables. This technique allows us to produce a closed-form invertible relation between the Boyer-Lindquist variables and the action-angle ones, while it generates in analytical closed form all the characteristic functions of the system as well. The expressed in the action-angle variable Hamiltonian system is employed to model an extreme mass ratio inspiral (EMRI), i.e. a binary system where a stellar compact object inspirals into a supermassive black hole due to gravitational radiation reaction. We consider the adiabatic evolution of an EMRI, for which the energy and angular momentum fluxes are computed by solving the Teukolsky equation in the frequency domain. To achieve this a new Teukolsky equation solver code was developed.

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“…We need a way to simulate inspiral waveforms for general EMRI's and investigate what the effects on these waveforms are when non-zero odd-parity multipoles S 2 , M 3 are present. Generating accurate waveforms for generic (Kerr) orbits is a difficult problem [36,37,38], that has so far been solved to adiabatic order [39] although with additionally an understanding of the full first order self-force [40]. It is an active area of research both to go beyond adiabatic order [41,42] as well as to improve computational efficiency [43,44,45].…”

Section: Generic Orbits: the Analytic Kludgementioning

confidence: 99%

Detecting equatorial symmetry breaking with LISA

Fransen

Mayerson

2022

Phys. Rev. D

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The equatorial symmetry of the Kerr black hole is generically broken in models of quantum gravity. Nevertheless, most phenomenological models start from the assumption of equatorial symmetry, and little attention has been given to the observability of this smoking gun signature of beyond-GR physics. Extreme mass-ratio inspirals (EMRIs), in particular, are known to sensitively probe supermassive black holes near their horizon; yet estimates for constraints on deviations from Kerr in space-based gravitational wave observations (e.g. with LISA) of such systems are currently based on equatorially symmetric models. We use modified "analytic kludge" waveforms to estimate how accurately LISA will be able to measure or constrain equatorial symmetry breaking, in the form of the lowest-lying odd parity multipole moments S 2 , M 3 . We find that the dimensionless multipole ratios such as S 2 /M 3 will typically be detectable for LISA EMRIs with a measurement accuracy of ∆(S 2 /M 3 ) ∼ 1%; this will set a strong constraint on the breaking of equatorial symmetry.

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Black Hole Perturbation Theory and Gravitational Self-Force

Cited by 41 publications

References 161 publications

Scattering in black hole backgrounds and higher-spin amplitudes. Part I

Scattering in black hole backgrounds and higher-spin amplitudes. Part I

Action-Angle formalism for extreme mass ratio inspirals in Kerr spacetime

Detecting equatorial symmetry breaking with LISA

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