Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

Energy Flux - Modified Harmonic Coords
Logs can be removed by the following shift on the particle world-lines:
ξ i 1 =
22 m
3
2 1m2 c6 r2 ni
r
ln ,
ξ i 2
= − 22
3
Under shift ξ, Accn of First particle shifts by
Rel Accn shifts by
δξa i = − m3 ν
+
r 4
δξa i 1 = ¨ ξ i 1 − ξ j
1
m1m 2 2
c 6 r 2 ni ln
r ′ 1
r
r ′ 2
− ξj
2 ∂ja i 1 .
110 ˙r 2 − 22v 2 n i − 44 ˙rv i ln
− 176
3 ˙r2 + 22
3 v2 − 22
3
m
r
.
n i + 44
3 ˙rvi
Log dependence in the above transformation exactly cancels the log dependence
of the acceleration in standard harmonic coordinates. Some 3PN coefficients
in the EOM are also modified and the final result for Accn in Modified Harm
Coords. agrees with that displayed in e.g. Mora Will
BRI-IHP06-I – p.33/??
r
r ′ 0