Energy-momentum conservation for gravitational two-body scattering in the post-linear approximation

Westpfahl, K.; Mohles, R; Simonis, H.

doi:10.1088/0264-9381/4/5/006

Cited by 15 publications

(25 citation statements)

References 6 publications

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“…Pioneering studies of the PM approximation [25][26][27][28][29][30][31][32][33][34][35] applied to the gravitational dynamics of massive bodies culminated in Westpfahl's computation, to 2PM order, of the scattering-angle function for an unbound system of two monopolar point masses (which could represent nonspinning BHs), via a direct assault on the nonlinear field equations in position space coupled with effective point-particle equations of motion [33]. In the intervening decades, this result stood alone and quite separated from primarily PN studies of bound coalescing binary systems and their GW emissions, until it was revisited in the latter context in Ref.…”

Section: Nonspinning-black-hole Scattering At Second Post-minkowsmentioning

confidence: 99%

“…As another example of this section's opening maxim (being particularly relevant for gravitational scattering), in an analytic treatment of the binary BH problem, we can trade the more easily handled post-Newtonian (PN) approximation [16][17][18][19][20][21][22][23][24] for the post-Minkowskian (PM) approximation [16,19,[25][26][27][28][29][30][31][32][33][34][35]: weak-field perturbation theory on a background flat Minkowski spacetime, without the further assumption of nonrelativistic speeds which would lead to the PN approximation. The PM approximation has recently been a subject of renewed interest concerning its applications to classical and quantum gravitational scattering of massive bodies and to the dynamics of bound binary systems [15,[36][37][38][39][40][41][42][43][44][45][46][47][48] (see also Refs.…”

Section: Introductionmentioning

confidence: 99%

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Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order

2019

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Recently, the gravitational scattering of two black holes (BHs) treated at the leading order in the weak-field, or post-Minkowskian (PM), approximation to general relativity has been shown to map bijectively onto a simpler effectively one-body process: the scattering of a test BH in a stationary BH spacetime. Here, for BH spins aligned with the orbital angular momentum, we propose a simple extension of that mapping to 2PM order. We provide evidence for the validity and utility of this 2PM mapping by demonstrating its compatibility with all known analytical results for the conservative local-in-time dynamics of binary BHs in the post-Newtonian (weak-field and slow-motion) approximation and, separately, in the test-BH limit. Our result could be employed in the construction of improved effective-one-body models for the conservative dynamics of inspiraling spinning binary BHs.

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Section: Nonspinning-black-hole Scattering At Second Post-minkowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order

2019

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“…The large mass-ratio case, which is relevant for space-based and third-generation ground-based detectors and requires a very accurate modeling of fast-motion effects, is one important example [34][35][36][37][38], which we will follow up elsewhere [39]. Here, we focus on the post-Minkowskian (PM) approximation (i.e., weak field and fast motion) [9,12,[40][41][42][43][44][45][46][47][48][49][50] applicable to scattering binaries (see also Refs. [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] for recent applications).…”

Section: Introductionmentioning

confidence: 99%

Energetics of two-body Hamiltonians in post-Minkowskian gravity

et al. 2019

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Advanced methods for computing perturbative, quantum-gravitational scattering amplitudes show great promise for improving our knowledge of classical gravitational dynamics. This is especially true in the weak-field and arbitrary-speed (post-Minkowskian, PM) regime, where the conservative dynamics at 3PM order has been recently determined for the first time, via an amplitude calculation. Such PM results are most relevantly applicable to relativistic scattering (unbound orbits), while bound/inspiraling binary systems, the most frequent sources of gravitational waves for the LIGO and Virgo detectors, are most suitably modeled by the weak-field and slow-motion (post-Newtonian, PN) approximation. Nonetheless, it has been suggested that PM results can independently lead to improved modeling of bound binary dynamics, especially when taken as inputs for effective-one-body (EOB) models of inspiraling binaries. Here, we initiate a quantitative study of this possibility, by comparing PM, EOB and PN predictions for the binding energy of a two-body system on a quasi-circular inspiraling orbit against results of numerical relativity (NR) simulations. The binding energy is one of the two central ingredients (the other being the gravitational-wave energy flux) that enters the computation of gravitational waveforms employed by LIGO and Virgo detectors, and for (quasi-)circular orbits it provides an accurate diagnostic of the conservative sector of a model. We find that, whereas 3PM results do improve the agreement with NR with respect to 2PM (especially when used in the EOB framework), it is crucial to push PM calculations at higher orders if one wants to achieve better performances than current waveform models used for LIGO/Virgo data analysis.

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“…The post-Minkowskian (PM) approach to gravitational interaction, which was pioneered some time ago [1][2][3][4][5][6][7][8], has been recently revived [9,10] and has undergone many developments both in classical gravity [11][12][13][14][15], and in the connection between classical gravity and quantum scattering amplitudes . The aim of the present paper is to extend the post-Minkowskian approach to tidal effects in binary systems.…”

Section: Introductionmentioning

confidence: 99%

Scattering of tidally interacting bodies in post-Minkowskian gravity

2020

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The post-Minkowskian approach to gravitationally interacting binary systems (i.e., perturbation theory in G, without assuming small velocities) is extended to the computation of the dynamical effects induced by the tidal deformations of two extended bodies, such as neutron stars. Our derivation applies general properties of perturbed actions to the effective field theory description of tidally interacting bodies. We compute several tidal invariants (notably the integrated quadrupolar and octupolar actions) at the first post-Minkowskian order. The corresponding contributions to the scattering angle are derived.

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Energy-momentum conservation for gravitational two-body scattering in the post-linear approximation

Cited by 15 publications

References 6 publications

Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order

Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order

Energetics of two-body Hamiltonians in post-Minkowskian gravity

Scattering of tidally interacting bodies in post-Minkowskian gravity

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