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General Relativity and Quantum Cosmology, gr-qc
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 we determine one of 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 non-local tail term in arbitrary dimensions. The
remaining ambiguity parameter is equivalent to the one appearing in the ADM
Hamiltonian approach.
