Next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form

Steinhoff, Jan; Hergt, Steven; Schäfer, Gerhard

doi:10.1103/physrevd.77.081501

Cited by 106 publications

(109 citation statements)

References 10 publications

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“…The next to leading spin-spin interaction was computed in [21] (see also [22,23,24]) in terms of 5 diagrams ( fig. 1 and fig.2 of [21]) which are quite analogous to the 5 diagrams for EIH in [1].…”

Section: Spin Interactionsmentioning

confidence: 99%

Non-relativistic gravitation: from Newton to Einstein and back

Kol¹,

Smolkin²

2008

Class. Quantum Grav.

142

191

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We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRGfields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-InfeldHoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.

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Section: Spin Interactionsmentioning

confidence: 99%

Non-relativistic gravitation: from Newton to Einstein and back

Kol¹,

Smolkin²

2008

Class. Quantum Grav.

142

191

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“…Some of these results were previously derived in [21][22][23][24] for the spin-orbit sector at 2.5PN order. The spin-spin gravitational potentials to 3PN were obtained within the EFT approach in [11][12][13][14]18], and in [25][26][27][28] and [29], using the ArnowittDeser-Misner (ADM) and harmonic gauge formalisms, respectively. The radiative multipole moments quadratic in the spin needed for the radiated power to 3PN, computed in [16] using the framework of [8,10,14,30], were also obtained in [29], although the comparison is pending.…”

Section: Introductionmentioning

confidence: 99%

Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

Galley

Leibovich

Porto³

et al. 2016

Phys. Rev. D

140

229

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We use the effective field theory (EFT) framework to calculate the tail effect in gravitational radiation reaction, which enters at the fourth post-Newtonian order in the dynamics of a binary system. The computation entails a subtle interplay between the near (or potential) and far (or radiation) zones. In particular, we find that the tail contribution to the effective action is nonlocal in time and features both a dissipative and a "conservative" term. The latter includes a logarithmic ultraviolet (UV) divergence, which we show cancels against an infrared (IR) singularity found in the (conservative) near zone. The origin of this behavior in the long-distance EFT is due to the point-particle limit-shrinking the binary to a pointwhich transforms a would-be infrared singularity into an ultraviolet divergence. This is a common occurrence in an EFT approach, which furthermore allows us to use renormalization group (RG) techniques to resum the resulting logarithmic contributions. We then derive the RG evolution for the binding potential and total mass/energy, and find agreement with the results obtained imposing the conservation of the (pseudo) stress-energy tensor in the radiation theory. While the calculation of the leading tail contribution to the effective action involves only one diagram, five are needed for the one-point function. This suggests logarithmic corrections may be easier to incorporate in this fashion. We conclude with a few remarks on the nature of these IR/UV singularities, the (lack of) ambiguities recently discussed in the literature, and the completeness of the analytic post-Newtonian framework.

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“…NLO spin-spin effects were already calculated a few years ago [22,23,[25][26][27][28][29]. Motivated by the above arguments, this paper attempts to improve the EOB Hamiltonian of Refs.…”

Section: Introductionmentioning

confidence: 95%

“…[19]). This may be due simply to the fact that spin effects beyond the leading order (LO) of the PN expansion series have been derived only in recent years [20][21][22][23][24][25][26][27][28][29][30][31][32], rather than to an intrinsic difficulty of the EOB approach to reproduce the spin interaction. Spin effects of coalescing BHBs have been included for the first time in the conservative part of the EOB formalism in Ref.…”

Section: Introductionmentioning

confidence: 97%

Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling for two nonprecessing black holes with aligned spins

Balmelli

Jetzer

2013

Phys. Rev. D

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The canonical Arnowitt-Deser-Misner (ADM) Hamiltonian with next-to-leading order spin-spin coupling [J. Steinhoff, S. Hergt, and G. Schäfer, Phys. Rev. D 77, 081501 (2008); 78, 101503 (2008)] is converted into the effective-one-body (EOB) formalism of [T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 78, 024009 (2008)] for the special case of spinning black hole binaries whose spins are aligned with the angular momentum. In particular, we propose to include the new terms by adding a dynamical term of next-to-leading order to the Kerr parameter squared entering the effective metric. The modified EOB Hamiltonian consistently reduces to the Kerr Hamiltonian as the mass ratio tends to zero; moreover, it predicts the existence of an innermost stable circular orbit. We also derive, for the general case of arbitrarily oriented spins but in the vanishing mass-ratio limit, a coordinate transformation that maps the next-to-leading order spin-spin contribution of the ADM Hamiltonian to the EOB Hamiltonian.

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Next-to-leading order gravitational spin(1)-spin(2) dynamics in Hamiltonian form

Cited by 106 publications

References 10 publications

Non-relativistic gravitation: from Newton to Einstein and back

Non-relativistic gravitation: from Newton to Einstein and back

Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution

Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling for two nonprecessing black holes with aligned spins

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