Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order

Physical Review D

Volumn 58, Issue 12, 1998, Pages 1240021-12400220

  Blanchet, Luc ^a   Faye, Guillaume ^a   Ponsot, Bénédicte ^a  

^a CNRS   (France)

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EID: 0000106151     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (61)

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54. Note that this solution represents only a particular solution of the equation we want to solve. However, any possible homogeneous solution must be regular in x and in the individual source points y! 2, and must have a compatible dimension. One can check that the only possibility is to add to g a simple numerical constant. This constant disappears after application of the spatial derivatives present in front of the term.
55. Note that the Hadamard finite part of the divergent integral is related to the value of r2drg at infinity [say, (r2arg)^], as computed in the same way as for the Hadamard finite part of a function at some finite-distance point, i.e., like in Eq. (3.6), by expanding r2drg when /-°° and taking the average over n of the term with zeroth power of r. We get finite part {(- l/47j-)/d3x/r,r2}= -(r2drg)x=rn/2. There is agreement with the value of the function Y defined by analytic continuation in Eqs. (4.22) and (4.23) of [39] for /=0.
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58. The solutions K] and //, satisfy the Poisson equations (6.3) in the sense of distributions, and tend to zero at infinity (|x|-rarr; + ∞).
59. 5 is zero.
60. 12) the metric is not simpler.
61. 2PN denotes the orbital phase and i the inclination angle.