Logarithmic tail contributions to the energy function of circular compact binaries
Résumé
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
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