Journal Article

PUBDB-2026-03296

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Black hole dynamics at fifth post-Newtonian order

Porto, R. A. (Corresponding author)DESY* ; Riva, M. M.

2026
Springer Heidelberg

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Please use a persistent id in citations: doi:10.1007/JHEP09(2026)075  doi:10.3204/PUBDB-2026-03296

Report No.: DESY 26-050; arXiv:2604.09545

Abstract: Using the worldline in-in effective action obtained in [1 ], we derive the total even-in-velocity relative impulse, scattering angle, and time delay at fifth post-Newtonian (5PN) order, including radiation-reaction and hereditary contributions at (G$^{5}$ν$^{2}$) and 𝒪(G$^{6}$ν$^{2}$). We introduce an isotropic-like description which, together with the associated losses of energy and angular momentum, fixes the evolution of the system entirely from scattering data. This framework opens the door to an unambiguous characterization of the underlying two-body dynamics solely in terms of scattering observables. Following [1 ], we isolate a conservative component using Feynman's i0$^{+}$ prescription. This sector contains both 'tail-like' and 'memory-like' contributions, the latter being intrinsically nonlocal in time and described by a double Principal-Value integral. Owing to the local-in-time character of the corresponding (in-in) action, we establish a systematic procedure that is consistent with Feynman's prescription while preserving the complete local dynamics. This provides a universal contribution to the conservative (isotropic) Hamiltonian at 5PN order and, as a byproduct, also fixes the value of the Effective One Body coefficients $\left\{{\overline{d} }_{5loc},{a}_{6loc}\right\}$ consistently with the Tutti-Frutti framework. For completeness, we analyse the 'γ-3' prescription introduced in recent post-Minkowskian computations. When implemented in our formalism, we find exact agreement over the overlapping regime of validity. In contrast, Feynman's prescription yields a (local) memory-like contribution with the opposite sign at (G$^{5}$ν$^{2}$). We also find that an analogous γ-3 rerouting at (G$^{6}$ν$^{2}$) would be incompatible with the conjecture that all π$^{2}$ terms arise solely from the potential region, while Feynman's formulation preserves this expectation.

Keyword(s): Classical Theories of Gravity ; Effective Field Theories ; Scattering Amplitudes

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Contributing Institute(s):

1. Theoretische Astroteilchenphysik (Z_THAT)

Research Program(s):

1. 613 - Matter and Radiation from the Universe (POF4-613) (POF4-613)
2. DFG project G:(GEPRIS)390833306 - EXC 2121 Das Quantisierte Universum II (390833306) (390833306)

Experiment(s):

1. Ultraviolet Transient Astronomy Satellite

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Porto Pereira, R. A. (Corresponding author)DESY* ; Riva, M. M.
Black Hole Dynamics at Fifth Post-Newtonian Order
(2026) [10.3204/PUBDB-2026-01113]2026     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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