Observables of a Test Mass along an Inclined Orbit in a Post-Newtonian-Approximated Kerr Spacetime Including the Linear and Quadratic Spin Terms

Hergt, Steven; Shah, Abhay; Schäfer, Gerhard

doi:10.1103/physrevlett.111.021101

Cited by 5 publications

(4 citation statements)

References 26 publications

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“…The radial epicyclic frequency for test particles in Kerr spacetime is frequently used when modeling phenomena in relativistic thin accretion disks [24]. For generic geodesics in Kerr spacetime, the PA is known in terms of elliptic integrals [25] and its PN expansion has been calculated explicitly [26]. Postgeodesic effects in the PA for nonspinning black holes in arXiv:1309.0544v3 [gr-qc] 16 Nov 2013 the small mass-ratio limit were obtained from the conservative gravitational self-force in Ref.…”

Section: Introductionmentioning

confidence: 99%

Periastron advance in spinning black hole binaries: comparing effective-one-body and numerical relativity

et al. 2013

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We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numericalrelativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinning particles onto the dynamics of an effective spinning particle in a (deformed) Kerr spacetime, fully symmetrized with respect to the two-body masses and spins, and (ii) the resummation, in the test-particle limit, of all post-Newtonian (PN) corrections linear in the spin of the particle. In fact, even when only the leading spin PN corrections are included in the effectiveone-body spinning Hamiltonian but all the test-particle corrections linear in the spin of the particle are resummed we find very good agreement with the numerical results (within the numerical error for equal-mass binaries and discrepancies of at most 1% for larger mass ratios). Furthermore, we specialize to the extreme mass-ratio limit and derive, using the equations of motion in the gravitational skeleton approach, analytical expressions for the periastron advance, the meridional Lense-Thirring precession and spin precession frequency in the case of a spinning particle on a nearly circular equatorial orbit in Kerr spacetime, including also terms quadratic in the spin.

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Section: Introductionmentioning

confidence: 99%

Periastron advance in spinning black hole binaries: comparing effective-one-body and numerical relativity

et al. 2013

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“…Substituting equations (33)- (35) into equation (32) then comparing the latter with equation (10), we have…”

Section: The Motion Of the Orbital Planementioning

confidence: 99%

“…Here 'the general motion' means the motion is not confined in the equatorial plane. Though the orbital period, the intrinsic periastron advance and the precession of the orbital plane of a test particle in the Kerr spacetime has been calculated to the 2.5PN order [35], the corresponding quasi-Keplerian equation for the general motion has not been reported yet.…”

Section: Introductionmentioning

confidence: 99%

The next-to-leading spin-orbit effects on the general motions in Kerr spacetime

Yang

Lin

2021

Phys. Scr.

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We derive the second-and-half post-Newtonian solution for the generally inclined motion of a test particle in Kerr spacetime when the effects of the spin-induced quadrupole are negligible. The next-to-leading order spin-orbit effects on the test particle’s motion are obtained, which are important in fitting the motions of the extremely-mass-ratio-inspiral systems and also calculating the gravitational wave radiated by this kind of systems at the second-and-half post-Newtonian order.

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“…Those are related to the recently introduced "Hill -inspired" variables (see[38] for reasons of this terminology) for compact binaries with spin.…”

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confidence: 99%

Eccentric motion of spinning compact binaries

Tessmer¹,

Schäfer

2014

Phys. Rev. D

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The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied which make a canonical perturbation theory easily treatable.

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Observables of a Test Mass along an Inclined Orbit in a Post-Newtonian-Approximated Kerr Spacetime Including the Linear and Quadratic Spin Terms

Cited by 5 publications

References 26 publications

Periastron advance in spinning black hole binaries: comparing effective-one-body and numerical relativity

Periastron advance in spinning black hole binaries: comparing effective-one-body and numerical relativity

The next-to-leading spin-orbit effects on the general motions in Kerr spacetime

Eccentric motion of spinning compact binaries

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