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The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach

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arxiv 2110.13822 v2 pith:T7F5V2IF submitted 2021-10-26 gr-qc

J. Blümlein , A. Maier , P. Marquard , G. Schäfer This is my paper
classification gr-qc
keywords contributionseffectivehamiltoniantermsapproachcalculatedynamicsexpansion
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abstract

Within an effective field theory method to general relativity, we calculate the fifth-order post--Newtonian (5 PN) Hamiltonian dynamics also for the tail terms, extending earlier work on the potential contributions, working in harmonic coordinates. Here we calculate independently all (local) 5 PN contributions to the tail terms using the in--in formalism, on which we give a detailed account. The five expansion terms of the Hamiltonian in the effective one body (EOB) approach, $q_{82}, q_{63}, q_{44}, \bar{d_5}$ and $a_6$, can all be determined from the local contributions to periastron advance $K^{\rm loc,h}(\hat{E},j)$, without further assumptions on the structure of the symmetric mass ratio, $\nu$, of the expansion coefficients of the scattering angle $\chi_k$. The $O(\nu^2)$ contributions to the 5 PN EOB parameters have been unknown in part before. We perform comparisons of our analytic results with the literature and also present numerical results on some observables.

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Cited by 4 Pith papers

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  1. N-body next-to-leading order gravitational spin-orbit interaction via effective field theory

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    The NLO gravitational spin-orbit Hamiltonian for N spinning bodies is computed via PN-EFT, with only three-body diagrams new beyond the binary case, and the result matches the known ADM Hamiltonian up to canonical tra...

  2. All-order structure of static gravitational interactions and the seventh post-Newtonian potential

    hep-th 2026-04 unverdicted novelty 6.0 of 10

    A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.

  3. Black Hole Dynamics at Fifth Post-Newtonian Order

    gr-qc 2026-04 unverdicted novelty 6.0 of 10

    Derives 5PN scattering observables and a conservative Hamiltonian contribution for black holes that determines EOB parameters d5loc and a6loc.

  4. Weak-field waveforms for generic relativistic orbits

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    Outlines a Schwinger-Keldysh path-integral framework that derives worldline equations of motion and computes weak-field gravitational waveforms independently for unspecified relativistic orbits.

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