Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
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Orbital Averaged AMF - ADM<br />
Us<strong>in</strong>g the QK representation of the orbit <strong>in</strong> ADM coord<strong>in</strong>ates and the<br />
<strong>in</strong>stantaneous angular momentum flux <strong>in</strong> ADM coord<strong>in</strong>ates, one<br />
transforms the expression for the magnitude of the angular<br />
momentum flux dJ /dt (r, ˙r 2 , v 2 ) ≡ |dJi/dt| to dJ /dt (E, h, er, u) where<br />
E is the conserved orbital energy and h is related the conserved<br />
angular momentum J as h = |J|/Gm. This expression up to 3PN order<br />
is schematically given as<br />
dJ<br />
dt<br />
= du<br />
ndt<br />
10<br />
N=2<br />
<br />
αN (et)<br />
+ βN(et)<br />
(1 − et cos u) N<br />
αN(E, h) = ν2<br />
G c 5 (−E)5 βN(E, h) .<br />
s<strong>in</strong> u<br />
(1 − et cos u) N + γN (et) ln(1 − et cos<br />
(1 − et cos u)<br />
βN (E, h) can be written down as a PN series but too long to be listed<br />
here.<br />
BRI-IHP06-I – p.76/??
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