The reduced Hamiltonian for next-to-leading-order spin-squared dynamics of general compact binaries

Hergt, Steven; Steinhoff, Jan; Schäfer, Gerhard

doi:10.1088/0264-9381/27/13/135007

Cited by 70 publications

(93 citation statements)

References 44 publications

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“…The initial momenta of the equalmass binaries, with the exception of X1 UU, were chosen by integrating the post-Newtonian equations of motion, as outlined in [22,23], with spin contributions to the Hamiltonian adapted from [24][25][26][27][28] (although we work in the ADM gauge, the results from harmonic gauge using effective-field theory [26] have been shown to be equivalent [29,30]), and the flux from [31]. For the X1 UU configuration, we used simpler quasicircular initial parameters with no initial ingoing radial momentum.…”

Section: Simulationsmentioning

confidence: 99%

Mergers of black-hole binaries with aligned spins: Waveform characteristics

et al. 2011

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We conduct a descriptive analysis of the multipolar structure of gravitational-radiation waveforms from equal-mass aligned-spin mergers, following an approach first presented in the complementary context of nonspinning black holes of varying mass ratio [1]. We find that, as with the nonspinning mergers, the dominant waveform mode phases evolve together in lock-step through inspiral and merger, supporting the previous waveform description in terms of an adiabatically rigid rotator driving gravitational-wave emission -an implicit rotating source (IRS). We further apply the latetime merger-ringdown model for the rotational frequency introduced in [1], along with an improved amplitude model appropriate for the dominant (2, ±2) modes. This provides a quantitative description of the merger-ringdown waveforms, and suggests that the major features of these waveforms can be described with reference only to the intrinsic parameters associated with the state of the final black hole formed in the merger. We provide an explicit model for the merger-ringdown radiation, and demonstrate that this model agrees to fitting factors better than 95% with the original numerical waveforms for system masses above ∼ 150M⊙. This model may be directly applicable to gravitational-wave detection of intermediate-mass black hole mergers.

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Section: Simulationsmentioning

confidence: 99%

Mergers of black-hole binaries with aligned spins: Waveform characteristics

et al. 2011

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“…order were added [45][46][47][48][49], and spin contributions have been extensively investigated [50][51][52][53][54][55][56][57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

et al. 2016

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The Fokker action governing the motion of compact binary systems without spins is derived in harmonic coordinates at the fourth post-Newtonian approximation (4PN) of general relativity.Dimensional regularization is used for treating the local UV divergences associated with point particles, followed by a renormalization of the poles into a redefinition of the trajectories of the point masses. Effects at the 4PN order associated with wave tails propagating at infinity are included consistently at the level of the action. A finite part procedure based on analytic continuation deals with the IR divergencies at spatial infinity, which are shown to be fully consistent with the presence of near zone tails. Our end result at 4PN order is Lorentz invariant and has the correct self-force limit for the energy of circular orbits. However, we find that it differs from the recently published result derived within the ADM Hamiltonian formulation of general relativity [T.Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.

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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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The reduced Hamiltonian for next-to-leading-order spin-squared dynamics of general compact binaries

Cited by 70 publications

References 44 publications

Mergers of black-hole binaries with aligned spins: Waveform characteristics

Mergers of black-hole binaries with aligned spins: Waveform characteristics

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

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

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