Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order

Tanay, Sashwat; Stein, Leo C.; Ghersi, José T. Gálvez

doi:10.1103/physrevd.103.064066

Cited by 19 publications

(47 citation statements)

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“…Second, we plan to compare with Post-Newtonian results based on the analysis in Refs. [43] and [44] as another validity check of our results. A catalog of these frequencies and how they vary with the parameters describing orbits and the small body's spin orientation is likely to be of use as waveform models for large mass ratio systems are developed and incorporated in gravitationalwave measurement pipelines.…”

Section: Summary and Future Worksupporting

confidence: 69%

Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits

Drummond,

Hughes

2022

Preprint

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In this paper, we continue our study of the motion of spinning test bodies orbiting Kerr black holes. Non-spinning test bodies follow geodesics of the spacetime in which they move. A test body's spin couples to the curvature of that spacetime, introducing a "spin-curvature force" which pushes the body's worldline away from a geodesic trajectory. The spin-curvature force is an important example of a post-geodesic effect which must be modeled carefully in order to accurately characterize the motion of bodies orbiting black holes. One motivation for this work is to understand how to include such effects in models of gravitational waves produced from the inspiral of stellar mass bodies into massive black holes. In this paper's predecessor, we describe a technique for computing bound orbits of spinning bodies around black holes with a frequency-domain description which can be solved very precisely. In that paper, we present an overview of our methods, as well as present results for orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is no more than O(S) out of the equatorial plane). In this paper, we apply this formulation to the fully generic case -orbits which are inclined and eccentric, with the small body's spin arbitrarily oriented. We compute the trajectories which such orbits follow, and compute how the small body's spin affects important quantities such as the observable orbital frequencies Ωr, Ω θ and Ω φ .

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Section: Summary and Future Worksupporting

confidence: 69%

Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits

Drummond,

Hughes

2022

Preprint

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“…This paper is a natural extension to our earlier work [17]. We compute the remaining fifth action variable using a novel method of extending the phase space by the introduction of new, unmeasurable phase space variables.…”

Section: Introductionmentioning

confidence: 96%

“…This line of questioning led two of us to probe the integrability (and therefore existence of action-angle variables) of the BBH system at 2PN in Ref. [17], wherein we found that a BBH system is indeed 2PN integrable when we applied the PN version of the Liouville-Arnold (LA) theorem (see Footnote 1), due to the existence of two new 2PN constants of motion we discovered. Since integrability precludes chaos (which would obstruct finding closed-form solutions), establishing integrability at 2PN instills hope towards finding a closed-form solutions at this order.…”

Section: Introductionmentioning

confidence: 98%

“…We initiated the action-angle calculation in Ref. [17], where we computed four (out of five) actions. In this paper, we compute the last action variable, and sketch how to transform to angle variables.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, in one of the appendices, we point out a loophole in the definition of PN integrability we presented in Ref. [17] and also provide an easy fix.…”

Section: Introductionmentioning

confidence: 99%

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Action-angle variables of a binary black-hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order

Tanay¹,

Cho²,

Stein³

2021

Preprint

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Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection through gravitational waves (GWs), with LIGO/Virgo/KAGRA, and LISA in the future. Solving the dynamics of a BBH system with arbitrary parameters without simplifications (like orbit-or precession-averaging) in closed-form is one of the most challenging problems for the GW community. One potential approach is using canonical perturbation theory which constructs perturbed action-angle variables from the unperturbed ones of an integrable Hamiltonian system. Having action-angle variables of the integrable 1.5 post-Newtonian (PN) BBH system is therefore imperative. In this paper, we continue the work initiated by two of us in [Tanay et al., Phys. Rev. D 103, 064066 (2021)], where we presented four out of five actions of a BBH system with arbitrary eccentricity, masses, and spins, at 1.5PN order. Here we compute the remaining fifth action using a novel method of extending the phase space by introducing unmeasurable phase space coordinates. We detail how to compute all the frequencies, and sketch how to explicitly transform to angle variables, which analytically solves the dynamics at 1.5PN. This lays the groundwork to analytically solve the conservative dynamics of the BBH system with arbitrary masses, spins, and eccentricity, at higher PN order, by using canonical perturbation theory.

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New horizons for fundamental physics with LISA

et al. 2022

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The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.

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Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order

Cited by 19 publications

References 48 publications

Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits

Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits

Action-angle variables of a binary black-hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order

New horizons for fundamental physics with LISA

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