Logarithmic tail contributions to the energy function of circular compact binaries

Luc Blanchet (1) , Stefano Foffa , François Larrouturou (1) , Riccardo Sturani

1 IAP - Institut d'Astrophysique de Paris

We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of general relativity. The logarithms come from the conservative part of nonlinear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory methods. We also determine all logarithmic terms at 7PN order, fixing a subleading logarithm from a tail-of-tail-of-tail process by comparison with self-force results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power n, appearing at (3n+1)PN order, and we resum the infinite series in a closed form. Half-integer PN orders enter the conservative dynamics starting at 5.5PN, but they do not generate logarithmic contributions up to next-to-next-to-leading order included. We nevertheless present their contribution at leading order in the small mass ratio limit.

Mots clés: General relativity; alternative theories of gravity; binary: compact; higher-order: 2; higher-order: 0; conservation law; effective field theory; gravitational radiation; renormalization group; general relativity; mass ratio; self-force; effect: nonlinear; gravitational radiation: emission; gravitation: weak field; numerical methods; numerical calculations

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Luc Blanchet, Stefano Foffa, François Larrouturou, Riccardo Sturani. Logarithmic tail contributions to the energy function of circular compact binaries. Physical Review D, 2020, 101 (8), pp.084045. ⟨10.1103/PhysRevD.101.084045⟩. ⟨hal-02447846⟩