Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
Celestial mechanics in Kerr spacetime
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by solving the Hamilton-Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies $\omega_{r}$, $\omega_{\theta}$ and $\omega_{\phi}$ associated with the radial, polar and azimuthal components of orbital motion. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this article, it is shown that the fundamental frequencies are geometric invariants and explicit formulas in terms of quadratures are derived. The numerical evaluation of these formulas in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters such as the semi-latus rectum $p$, the eccentricity $e$ or the inclination parameter $\theta_{-}$ are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulas.
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background 2representative citing papers
Disk-induced dissipation drives rapid orbital plane alignment followed by slower eccentricity damping in extreme mass-ratio inspirals, with relativistic effects producing accumulating deviations from Keplerian orbits even at large separations.
Introduces a gauge transformation framework for BMS frames in multiscale black hole perturbation theory on Kerr that incorporates memory effects and avoids infrared divergences.
Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
Derives the fifth action for 1.5PN BBH with arbitrary eccentricity, spins, and masses, completing action-angle variables for analytical dynamics solution.
For most studied EMRI orbits, omitting 3:2, 2:1, 4:3, or 3:1 resonance crossings causes significant SNR loss and Fisher biases exceeding 1σ, with coefficient signs and amplitudes controlling the effect.
citing papers explorer
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Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order
Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.
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Orbital evolution of asymmetric binaries within accreting environments
Disk-induced dissipation drives rapid orbital plane alignment followed by slower eccentricity damping in extreme mass-ratio inspirals, with relativistic effects producing accumulating deviations from Keplerian orbits even at large separations.
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The Bondi--Sachs gauge, BMS frames, and memory in black hole perturbation theory
Introduces a gauge transformation framework for BMS frames in multiscale black hole perturbation theory on Kerr that incorporates memory effects and avoids infrared divergences.
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The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes
Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
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Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
Derives the fifth action for 1.5PN BBH with arbitrary eccentricity, spins, and masses, completing action-angle variables for analytical dynamics solution.
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Parameter-estimation bias induced by transient orbital resonances in extreme-mass-ratio inspirals
For most studied EMRI orbits, omitting 3:2, 2:1, 4:3, or 3:1 resonance crossings causes significant SNR loss and Fisher biases exceeding 1σ, with coefficient signs and amplitudes controlling the effect.