Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry

Fujita, Ryuichi; Isoyama, Soichiro; Tiec, Alexandre Le; Nakano, Hiroyuki; Sago, Norichika; Tanaka, Takahiro

doi:10.1088/1361-6382/aa7342

Cited by 50 publications

(57 citation statements)

References 237 publications

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“…1, we see that E 1st law SF agrees fairly well with our results for E SF , but the inset shows that the disagreement is larger than our numerical uncertainty. This is not surprising: although various formulations of the FLBM have been derived [54,55,[57][58][59][60], none of them precisely applies to our particular scenario. Each of them is derived for a fully conservative spacetime with an exact helical Killing vector k µ = (1, 0, 0, Ω), corresponding to a binary in an eternally circular orbit.…”

Section: E(y)mentioning

confidence: 97%

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Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries

et al. 2020

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Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.

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Section: E(y)mentioning

confidence: 97%

“…In addition to that critical difference, the version of the FLBM that is most applicable to our scenario, derived in [60], does not define the binding energy from the system's Bondi mass. Instead, as alluded to above, it uses a local, mechanical energy.…”

Section: E(y)mentioning

confidence: 99%

Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries

et al. 2020

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“…According to the first law(s) of spinning binary (conservative) mechanics, as developed by Le Tiec and collaborators e.g. in [65,67], for a circular orbit, "on shell," we should have…”

Section: The First Law Of Aligned-spin Circular-orbit Binary Mechmentioning

confidence: 99%

Test black holes, scattering amplitudes, and perturbations of Kerr spacetime

Siemonsen

Vines

2020

Phys. Rev. D

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It has been suggested that amplitudes for quantum higher-spin massive particles exchanging gravitons lead, via a classical limit, to results for scattering of spinning black holes in general relativity, when the massive particles are in a certain way minimally coupled to gravity. Such limits of such amplitudes suggest, at least at lower orders in spin, up to second order in the gravitational constant G, that the classical aligned-spin scattering function for an arbitrary-mass-ratio two-spinning-blackhole system can be obtained by a simple kinematical mapping from that for a spinning test black hole scattering off a stationary background Kerr black hole. Here we test these suggestions, at orders beyond the reach of the post-Newtonian and post-Minkowskian results used in their initial partial verifications, by confronting them with results from general-relativistic "self-force" calculations of the linear perturbations of a Kerr spacetime sourced by a small orbiting body, here considering only results for circular orbits in the equatorial plane. We translate between scattering and circular-orbit results by assuming the existence of a local-in-time canonical Hamiltonian governing the conservative dynamics of generic (bound and unbound) aligned-spin orbits, while employing the associated first law of spinning binary mechanics. We confirm, through linear order in the mass ratio, some previous conjectures which would begin to fill in the spin-dependent parts of the conservative dynamics for arbitrary-mass-ratio aligned-spin binary black holes at the fourth-and-a-half and fifth post-Newtonian orders.

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“…The first law of binaries was originally formulated in a PN context. Later work [57][58][59] established Hamiltonian formulations of the first law directly in the context of self-force theory.…”

Section: Introductionmentioning

confidence: 99%

Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime

et al. 2019

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For a Schwarzchild black hole of mass M , we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius r = 4GM/c 2 . When the particle is endowed with a small mass, µ M , it experiences an effective gravitational self-force, whose conservative piece shifts the critical value of the angular momentum and the frequency of the asymptotic circular orbit away from their geodesic values. By directly integrating the self-force along the orbit (ignoring radiative dissipation), we numerically calculate these shifts to O(µ/M ).Our numerical values are found to be in agreement with estimates first made within the Effective One Body formalism, and with predictions of the first law of black-hole-binary mechanics (as applied to the asymptotic circular orbit). Our calculation is based on a time-domain integration of the Lorenz-gauge perturbation equations, and it is a first such calculation for an unbound orbit. We tackle several technical difficulties specific to unbound orbits, illustrating how these may be handled in more general cases of unbound motion. Our method paves the way to calculations of the self-force along hyperbolic-type scattering orbits. Such orbits can probe the two-body potential down to the "light ring", and could thus supply strong-field calibration data for eccentricity-dependent terms in the Effective One Body model of merging binaries.

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Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry

Cited by 50 publications

References 237 publications

Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries

Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries

Test black holes, scattering amplitudes, and perturbations of Kerr spacetime

Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime

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