Abstract
We calculate the potential contributions of the motion of binary mass systems in gravity to the fifth post–Newtonian order ab initio using coupling and velocity expansions within an effective field theory approach based on Feynman amplitudes starting with harmonic coordinates and using dimensional regularization. Furthermore, the singular and logarithmic tail contributions are calculated. We also consider the non–local tail contributions. Further steps towards the complete calculation are discussed. We calculate all but the rational O(ν2) contributions to the bound state energy for circular motion and periastron advance K(Eˆ,j). Comparisons are given to results in the literature.
Highlights
The measurement of gravitational wave signals from merging black holes and neutron stars [1] has been a recent milestone in astrophysics
SNRGR,bulk is the same as the general relativity bulk action SGR,bulk from Eq (20), but without the potential contributions to the metric. Both VNZ and the effective stress–energy tensor T μν are fixed by requiring that the non–relativistic general relativity (NRGR) action produces the same predictions as the asymptotic expansion of the full theory
We have presented the 5PN potential contributions to the Hamiltonian of binary motion in gravity starting form the harmonic gauge and a part of the 5PN tail term
Summary
The measurement of gravitational wave signals from merging black holes and neutron stars [1] has been a recent milestone in astrophysics. In binary Hamiltonian dynamics the level of the 4th post–Newtonian (PN) order has been fully understood and agreeing results have been obtained using a variety of different computation techniques in quite a series of gauges which lead to identical predictions in all key observables [3,4,5,6,7,8,9] It has been shown by applying canonical transformations [9], that all descriptions are dynamically equivalent. In the case of the tail terms one first applies the multi–pole expansion valid for the far zone [3,13,15,25,27,31,32,33,34,35,36,37,38,39] to the respective post–Newtonian order and applies EFT methods to calculate their contribution, cf [40]. As well we present longer formulae, which are used in the present calculation
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