Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

Abstract

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed by comparison with gravitational self-force (GSF) calculations of the conserved energy and periastron advance for circular orbits in the test-mass limit. In the present paper together with a companion paper, we determine both these ambiguities from first principle, by means of dimensional regularization. Our computation is thus entirely defined within the dimensional regularization scheme, for treating at once the IR and ultra-violet (UV) divergencies. In particular, we obtain crucial contributions coming from the Einstein-Hilbert part of the action and from the non-local tail term in arbitrary dimensions, which resolve the ambiguities.

25 pages, published version

References in corpus (6)

• Fourth post-Newtonian effective one-body dynamics
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Self-force corrections to the periapsis advance around a spinning black hole

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