2014/01/31 by Thibault Damour, Piotr Jaranowski, Gerhard Schäfer · 1 citation
Physics and Astronomy · Mathematics · #gr-qc #astro-ph.HE #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.89.064058
published as Phys. Rev. D 89, 064058 (2014) · Minor amendments added; misprints removed; identical with published version. 18 pages
arxiv created 2014/03/28 · arxiv updated 2014/04/02
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.Schäfer, 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 Poincaré-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.