REVIEW 13 cited by
Celestial mechanics in Kerr spacetime
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
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.
Forward citations
Cited by 13 Pith papers
-
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.
-
Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
Closed-form action and frequency formulas for spinning particles in Kerr spacetime are matched to the 1.5 post-Newtonian Hamiltonian of spinning binaries, yielding a gauge-invariant action dictionary.
-
Quadrupolar tidal effects destroy the integrability of black hole geodesics: analytic proof and numerical evidence of chaos
Leading-order tidally induced quadrupoles destroy Kerr geodesic integrability: no polynomial deformation of the Carter constant is conserved for generic Love couplings and Kerr spin.
-
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 ...
-
Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown
Quadratic-in-spin MPTD dynamics in type-D Einstein spacetimes with Killing–Yano symmetry admits five commuting first integrals—hence Liouville–Arnold integrability—only when the spin-induced quadrupole deformability p...
-
Post-Newtonian expansion of gravitational energy and angular momentum fluxes: inclined spherical orbits about a Kerr black hole
The paper derives 12PN flux formulas for inclined spherical Kerr orbits, exact in spin and inclination.
-
The significance of first post-adiabatic contributions for scalar charge measurements with intermediate and extreme mass ratio inspirals
Neglecting 1PA gravitational self-force biases intrinsic EMRI parameters while scalar-charge inference remains robust; pure-GR templates produce large biases and underestimated errors on charged signals.
-
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.
-
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.
-
Tidal perturbations of an extreme mass ratio inspiral around a Kerr black hole
A closed-form Kerr metric under slow quadrupolar tides yields spin-dependent tidal shifts of the ISCO and light ring, with larger shifts for retrograde orbits around fast-spinning holes.
-
Observable signature of magnetic tidal coupling in hierarchical triple systems
Magnetic tidal fields from a supermassive black hole trigger new orbital resonances in a companion compact binary, boosting eccentricity and altering its gravitational-wave signal.
-
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.
-
Parameter-estimation bias induced by transient orbital resonances in extreme-mass-ratio inspirals
Neglecting transient orbital resonances in EMRIs causes significant SNR losses and biases in recovered parameters, with the sign and amplitude of resonance-induced changes to integrals of motion being critical.
Discussion (0). Continue with ORCID to comment.