Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem

Damour, Thibault; Jaranowski, P.; Schäfer, Gerhard

doi:10.1103/physrevd.62.021501

Cited by 304 publications

(684 citation statements)

References 15 publications

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“…(5.11) of Ref. [48] in terms of the angular momentum density j for circular orbits and the symmetric mass-ratio m 1 m 2 =ðm 1 þ m 2 Þ 2 , where m 1 and m 2 are the masses of the two bodies, as…”

Section: Appendix A: Pn Periastron Advancementioning

confidence: 99%

“…In post-Newtonian approximations, the periastron advance was calculated to 3PN order in [48] for circular orbits in terms of the frequency-related parameter x. In the nonspinning circular case, the explicit expression for K is given by Eq.…”

Section: Appendix A: Pn Periastron Advancementioning

confidence: 99%

“…This allows us in Section IV to estimate the periastron advance for these runs from the ratio of the orbital frequency to the radial frequency as well as the periastron advance of a set of quasicircular nonspinning binaries of mass ratios 2, 3, 4 and 6. The numerically estimated periastron advance is then compared to the 3PN formula of the periastron advance [29,39,48].…”

Section: Introductionmentioning

confidence: 99%

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Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations

et al. 2010

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We compare different methods of computing the orbital eccentricity of quasicircular binary black-hole systems using the orbital variables and gravitational-wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational-wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of nonspinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations.

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Section: Appendix A: Pn Periastron Advancementioning

confidence: 99%

Section: Appendix A: Pn Periastron Advancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations

et al. 2010

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“…One of those quantities calculated in self-force theory is Detweiler's redshift invariant, ∆U , the linear-in-mass-ratio correction to the time component of the 4-velocity of the light compact object [10]. The PN coefficients of ∆U are directly related to those of the linear-in-mass-ratio portion of the binding energy and angular momentum of the binary, as well as to the radial potential that is fundamental to the EOB formalism, as was demonstrated in [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Experimental mathematics meets gravitational self-force

2015

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It is now possible to compute linear in mass-ratio terms in the post-Newtonian (PN) expansion for compact binaries to very high orders using linear black hole perturbation theory applied to various invariants. For instance, a computation of the redshift invariant of a point particle in a circular orbit about a black hole in linear perturbation theory gives the linear-in-mass-ratio portion of the binding energy of a circular binary with arbitrary mass ratio. This binding energy, in turn, encodes the system's conservative dynamics. We give a method for extracting the analytic forms of these post-Newtonian coefficients from high-accuracy numerical data using experimental mathematics techniques, notably an integer relation algorithm. Such methods should be particularly important when the calculations progress to the considerably more difficult case of perturbations of the Kerr metric. As an example, we apply this method to the redshift invariant in Schwarzschild. Here we obtain analytic coefficients to 12.5PN, and higher-order terms in mixed analytic-numerical form to 21.5PN, including analytic forms for the complete 13.5PN coefficient, and all the logarithmic terms at 13PN. We have computed the individual modes to over 5000 digits, of which we use at most 1240 in the present calculation. At these high orders, an individual coefficient can have over 30 terms, including a wide variety of transcendental numbers, when written out in full. We are still able to obtain analytic forms for such coefficients from the numerical data through a careful study of the structure of the expansion. The structure we find also allows us to predict certain "leading logarithm"-type contributions to all orders. The additional terms in the expansion we obtain improve the accuracy of the PN series for the redshift observable, even in the very strongfield regime inside the innermost stable circular orbit, particularly when combined with exponential resummation.

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“…These include: (i) the blurred, adiabatic transition from the inspiral to a plunge, which is merely a continuation of the inspiral, (ii) the extremely short merger phase, (iii) the simplicity of the merger waveform (i.e., the absence of high-frequency features in it, with the burst of radiation produced at the merger being filtered by the potential barrier surrounding the newborn BH), (iv) estimates of the radiated energy during the last stages of inspiral, merger and ringdown (0.6% to 5% of the binary total mass depending on BH spin magnitude) and spin of the final BH (e.g., 0.8M 2 BH for an equal-mass binary, M BH being the final BH mass), and (v) prediction that a Kerr BH will promptly form at merger even when BHs carry spin close to extremal. Soon after its inception, the EOB model was extended to include leading-order spin effects [271] and higher-order PN terms that meanwhile became available [272].…”

Section: The Effective-one-body Formalismmentioning

confidence: 99%