Abstract
We calculate the motion of binary mass systems in gravity up to the fourth post–Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying dimensional regularization. We construct the canonical transformations to ADM coordinates and to effective one body theory (EOB) to compare with other approaches. We show that intermediate poles in the dimensional regularization parameter ε vanish in the observables and the classical theory is not renormalized. The results are illustrated for a series of observables for which we agree with the literature.
Highlights
Precise predictions for observables describing the merging of two heavy astrophysical objects like black holes or neutron stars are very important [1]
Methods of non-relativistic effective field theory [2,3,4,5,6,7,8,9] allow to calculate the equations of motion of a binary mass system within the post– Newtonian (PN) approach
Using the effective field theory approach of Einstein–Hilbert gravity in the post–Newtonian orders, the harmonic coordinates belong to a class in which pole terms already occur at the level of 3PN
Summary
Precise predictions for observables describing the merging of two heavy astrophysical objects like black holes or neutron stars are very important [1]. By applying canonical transformations one may map the Hamiltonian in harmonic coordinates into a class of pole–free Hamiltonians at 3PN, to which the ADM and EOB Hamiltonians belong. This is the case at 4PN when accounting for the tail terms before. In an appendix we present the general Ddimensional Hamiltonian in harmonic coordinates up to O(ε) in explicit form, which is important for higher post–Newtonian calculations
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