Fourth post-Newtonian effective one-body dynamics

Thibault Damour, Piotr Jaranowski, and Gerhard Schäfer
Phys. Rev. D 91, 084024 – Published 10 April 2015

Abstract

The conservative dynamics of gravitationally interacting two-point-mass systems has been recently determined at the fourth post-Newtonian (4PN) approximation [T. Damour, P. Jaranowski, and G. Schäfer, Phys. Rev. D 89, 064058 (2014)], and found to be nonlocal in time. We show how to transcribe this dynamics within the effective one-body (EOB) formalism. To achieve this EOB transcription, we develop a new strategy involving the (infinite-)order-reduction of a nonlocal dynamics to an ordinary action-angle Hamiltonian. Our final, equivalent EOB dynamics comprises two (local) radial potentials, A(r) and D¯(r), and a nongeodesic mass-shell contribution Q(r,pr) given by an infinite series of even powers of the radial momentum pr. Using an effective action technique, we complete our 4PN-level results by deriving two different, higher-order conservative contributions linked to tail-transported hereditary effects: the 5PN-level EOB logarithmic terms, as well as the 5.5PN-level, half-integral terms. We compare our improved analytical knowledge to previous, numerical gravitational-self-force computation of precession effects.

  • Figure
  • Received 25 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.084024

© 2015 American Physical Society

Authors & Affiliations

Thibault Damour*

  • Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France

Piotr Jaranowski

  • Faculty of Physics, University of Białystok, Ciołkowskiego 1L, 15–245 Białystok, Poland

Gerhard Schäfer

  • Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Pl. 1, 07743 Jena, Germany

  • *damour@ihes.fr
  • p.jaranowski@uwb.edu.pl
  • gos@tpi.uni-jena.de

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Issue

Vol. 91, Iss. 8 — 15 April 2015

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