Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems

By T. Damour, P. Jaranowski, G. Schāfer. 2014

215 citations recorded by the source corpus.

We complete the analytical determination, at the 4th post-Newtonian (4PN) approximation, of the conservative dynamics of gravitationally interacting two-point-mass systems. This completion is obtained by resolving the infra-red ambiguity which had blocked a previous 4PN calculation [P. Jaranowski and G. Sch\"afer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN breakdown of the usual near-zone expansion due to infinite-range tail-transported temporal correlations found long ago [L. Blanchet and T. Damour, Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincar\'e-invariant 4PN-accurate effective action for two masses, which mixes instantaneous interaction terms (described by a usual Hamiltonian) with a (time-symmetric) nonlocal-in-time interaction.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3bbe98b44befdc47c24291b8776bff2130dd790d

How researchers see this paper

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In Astronomy and Astrophysics

1. T. Damour
2. G. Kalin
3. Rafael A. Porto
4. J. Steinhoff
5. R. Roiban
6. A. Luna
7. J. Plefka
8. Z. Bern

In Atomic and Molecular Physics, and Optics

1. Rafael A. Porto
2. G. Kalin
3. J. Steinhoff
4. M. Levi
5. Z. Bern
6. R. Roiban
7. C. Cheung
8. Chia-Hsien Shen

Citations in the corpus

• Spinning black hole binary dynamics, scattering amplitudes, and effective field theory (2020, methodology): “In the inspiral phase, we have the traditional post-Newtonian (PN) approximation using methods in classical gravity [5, 6] and the nonrelativistic general relativity (NRGR) formalism [7, 8] based on effective field theory (EFT), as well as the post-Minkowskian (PM) expansion [9–17].”
• Classical black hole scattering from a worldline quantum field theory (2020, background): “The state of the art is 4PN level for the potential [22–32], parts of 5PN [33–35] and 6PN [36–41], and 3PN [42–44] for the gravitational radiation emitted from a quasi-circular inspiral (see also ref.”
• Post-Minkowskian effective field theory for conservative binary dynamics (2020, methodology): “As a result, joining an effort which involves also more ‘traditional’ methods [18–24], the present state-of-the-art in NRGR is at the fourth PN (4PN) order of accuracy in the conservative sector for non-spinning bodies [8, 17, 25– 31], which includes also contributions induced from (conservative) ra”
• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme (2015, background): “5PN order, should be obtained at least to 4PN order, which was recently completed in the non-spinning case [9].”
• Gravitational scattering, post-Minkowskian approximation, and effective-one-body theory (2016, background): “Therefore, the exact computation of a certain term in the PM expansion of χ (as we shall report below) represents an information about the two-body dynamics which goes beyond all the present PN knowledge (which is limited to the 4PN level [36], [30]), though it evidently misses some of the informati”
• Black hole binary dynamics from the double copy and effective theory (2019, background): “sformations, which we solved up to 4PN order. Given the canonical transformation built above, the remaining free coecients can be adjusted to obtain a perfect match between H4PN in Eq.(8.41) of Ref. [35,36] and our result in Eq. (10.8), H4PN(R;P) O(G3v4) = H3PM(r;p) O(G3v4) ; (11.6) valid up to O(G3”
• High-energy gravitational scattering and the general relativistic two-body problem (2017, methodology): “The conservative two-body dynamics was derived, successively, at the second post-Newtonian (2PN) [14, 15], third postNewtonian (3PN) [16], and fourth post-Newtonian (4PN) [17] levels (with a crucial 4PN contribution having been derived by black-hole perturbation theory [18]).”
• The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “) At 4PN order we also find time non-locality in the effective action, due to hereditary effects [111, 112].”
• From boundary data to bound states (2019, methodology): “Using the powerful EFT machinery, as well as other methodologies [15–18], the current level of accuracy in the PN framework has achieved the next-tonext-to-next-to-next-to-leading order (N4LO) in the conservative sector, or four-loops [19–23], and up to five-loops in the static limit [24, 25].”