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

Tanay, Sashwat; Cho, Gihyuk; Stein, Leo C.

doi:10.48550/arxiv.2110.15351

Cited by 4 publications

(25 citation statements)

References 29 publications

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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: 67%

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: 67%

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

Drummond,

Hughes

2022

Preprint

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“…[41], with action angle variables presented explicitly in Ref. [42]. In the extreme mass ratio limit, numerical studies in both Schwarzschild [89] and Kerr [90,91] backgrounds found evidence for chaotic motion.…”

Section: B Past Workmentioning

confidence: 98%

“…The effective-onebody (EOB) framework synthesizes elements from post-Newtonian, extreme-mass-ratio, and numerical relativity results in order to construct a useful prescription for modeling inspirals across a wide parameter space. The dynamics of comparable mass binaries with spinning components has been explored in many post-Newtonian studies [36][37][38][39][40][41][42]; complementary to this, binaries with spinning members have been investigated extensively in numerical relativity simulations [43][44][45][46][47][48]. Considerable work has also been undertaken to develop EOB models that include spin and quantify their reliability [24][25][26][27][49][50][51]; a comparison of spinning effective one body Hamiltonians can be found in Ref.…”

Section: B Past Workmentioning

confidence: 99%

Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits

Drummond,

Hughes

2022

Preprint

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Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Accurate models of such systems require post-geodesic corrections to this motion. Post-geodesic effects that drive the small body away from the geodesic include the gravitational self force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for precisely computing bound orbits of spinning bodies about black holes. Our analysis builds off of pioneering work by Witzany which demonstrated how to describe the motion of a spinning body to linear order in the small body's spin. Exploiting the fact that in the large mass-ratio limit spinning-body orbits are close to geodesics (in a sense that can be made precise) and using closed-form results due to van de Meent describing precession of the small body's spin along black hole orbits, we develop a frequency-domain formulation of the motion which can be solved very precisely. We examine a range of orbits with this formulation, focusing in this paper on orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is O(S) out of the equatorial plane), but for which the small body's spin is arbitrarily oriented. We discuss generic orbits with general small-body spin orientation in a companion paper. We characterize the behavior of these orbits, contrasting them with geodesics, and show how the small body's spin shifts the frequencies Ωr and Ω φ which affect orbital motion. These frequency shifts change accumulated phases which are direct gravitational-wave observables, illustrating the importance of precisely characterizing these quantities for gravitational-wave observations.

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“…These lecture notes are based on Refs. [1,2,3] which aim to give closed-form solutions to the spinning, eccentric binary black hole dynamics at 1.5PN via two different equivalent ways: (i) the standard way of integrating the Hamilton's equations and (ii) using action-angle variables.…”

Section: Introductionmentioning

confidence: 99%

“…Accompanying the above three papers (Refs. [1,2,3]), and these lecture notes is a Mathematica package [18]. This package can do the following…”

Section: Introductionmentioning

confidence: 99%

Integrability and action-angle-based solution of the post-Newtonian BBH system (lecture notes)

Tanay¹

2022

Preprint

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

Cited by 4 publications

References 29 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

Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits

Integrability and action-angle-based solution of the post-Newtonian BBH system (lecture notes)

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