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Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries

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arxiv gr-qc/0010040 v3 pith:VLBZ6Z3Z submitted 2000-10-10 gr-qc

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keywords approachesharmonic-coordinatesdifferentdynamicsequivalencepost-newtoniansystemsthird
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The third post-Newtonian approximation to the general relativistic dynamics of two point-mass systems has been recently derived by two independent groups, using different approaches, and different coordinate systems. By explicitly exhibiting the map between the variables used in the two approaches we prove their physical equivalence. Our map allows one to transfer all the known results of the Arnowitt-Deser-Misner (ADM) approach to the harmonic-coordinates one: in particular, it gives the value of the harmonic-coordinates Lagrangian, and the expression of the ten conserved quantities associated to global Poincar\'e invariance.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM

    gr-qc 2024-12 conditional novelty 7.0 of 10

    The authors obtain, for the first time, 3PN-accurate eccentric-orbit fluxes, radiation-reaction force, and waveform modes in the effective-one-body formalism, and use them to build the SEOBNRv5EHM inspiral model.

  2. Heterotic Footprints in Classical Gravity: PM dynamics from On-Shell soft amplitudes at one loop

    hep-th 2025-10 unverdicted novelty 6.0 of 10

    Derives conservative potential and scattering angle for charged black holes in EMD theory via one-loop soft amplitudes, showing IR finiteness after Lippmann-Schwinger treatment and smooth reduction to GR.

  3. Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter

    hep-th 2023-05 unverdicted novelty 6.0 of 10

    Computes 1PN conservative dynamics for gravitational/EM/Proca fields and 2PN for scalar, plus radiation effects from axion-photon coupling at high PN orders in binary black hole systems with dark matter.

  4. Classical Black Hole Scattering to Celestial Amplitudes in Effective Theories of Gravity

    hep-th 2026-08 conditional novelty 3.0 of 10

    A doctoral thesis reproduces the author's published post-Newtonian and post-Minkowskian two-body observables and celestial amplitudes in scalar-tensor, Chern-Simons, Einstein-Maxwell-dilaton, and quadratic gravity.

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