Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
3PN Mass Quadrupole for ICB where Iij = ν m +2 A = 1 + 1 c 2 A − 24 7 C v 2 ν c 5 r ˙r 24 + c2 7 29 G 2 m 2 r 2 ν c 5 − 29 ν 14 + 42 1 B = 1 (· · ·) + (· · ·) c4 c6 11 11 1 − ν + 21 7 c2 Gm r + v 2 41 337 − 126 126 + 1 C = 1 (· · ·) + (· · ·) c4 c6 − 2 6 1 + ν + 7 7 c2 v 2 + G m − r 155 108 ˙r G 2 m 2 r + G m 106 x 〈ixj〉 + B r2 c2 v 〈ivj〉 r x 〈iv j〉 − 5 7 , + 8 7 ν 335 985 − ν − 27 189 189 ν2 733 ν + 126 ν2 + ˙r 2 5 25 − 63 63 + 4057 756 − 13 63 + 101 63 ν + 209 108 ν2 209 ν − 63 ν2 + 1 (· · ·) c4 25 ν + 63 ν2 BRI-IHP06-I – p.27/??
Instantaneous Terms dE dt inst dE dt = G c5 1 5 I(3) ij I(3) ij + 1 c 2 + 8G 5c 5 + 2G 5c 1 3 ɛabi + 1 c 6 1 = 189 I(4) ijkI(4) ijk I (3) ij I(3) 5 ij I (4) aj dE dt + 16 45 inst J (3) ij dE + dt (3) J ij + 1 c4 hered IijW (5) + 2I (1) ij W (4) − 2I (3) − 4 7 I(5) ai I(1) aj J (1) b + I(5) aj Jb − I(4) ai I(2) aj 1 594000 I(6) ijkmn I(6) ijkmn . 1 9072 I(5) ijkm I(5) ijkm ij W (2) − I (4) (1) ij W 4 − 7 I(3) ai I(3) aj + 1 7 I(6) ai Iaj+ 1 + 84 4 (5) (5) + J J + O(8) . 14175 ijkm ijkm (4) (4) J ijkJ ijk BRI-IHP06-I – p.28/??
- Page 1 and 2: Gravitational Waves from Inspiralli
- Page 3 and 4: Introduction Inspiralling Compact B
- Page 5 and 6: Kozai Mechanism One proposed astrop
- Page 7 and 8: Kozai Mechanism, Globular Clusters
- Page 9 and 10: Kicks, Eccentricity Compact binarie
- Page 11 and 12: Related Earlier Work ∗ Peters and
- Page 13 and 14: Earlier Work ∗ GW from an eccentr
- Page 15 and 16: FF as fn of initial eccentricity e0
- Page 17 and 18: Eccentric Signal Plots of s(t) (up
- Page 19 and 20: The Generation Modules Generation p
- Page 21 and 22: Present Work Represent GW from a bi
- Page 23 and 24: PN order of Multipoles For a given
- Page 25 and 26: Radiative moments - Source moments
- Page 27: 3PN EOM for ICB a i = dvi dt AE = 1
- Page 31 and 32: 3PN Instantaneous Terms dE dt 2PN
- Page 33 and 34: Transfn of World lines Having obtai
- Page 35 and 36: Energy Flux - Modified Harmonic Coo
- Page 37 and 38: 3PN generalised Quasi-Keplerian rep
- Page 39 and 40: 3PN generalised Quasi-Keplerian rep
- Page 41 and 42: 3PN GQKR - Mhar n = (−2E) 3/2 +11
- Page 43 and 44: 3PN GQKR - Mhar + Φ = 2 π 70 16
- Page 45 and 46: Orbital average - Energy flux -MHar
- Page 47 and 48: Orbit Averaged Energy Flux - MHar <
- Page 49 and 50: Comments Note: No term at 2.5PN. 2.
- Page 51 and 52: Comments Useful internal consistenc
- Page 53 and 54: Gauge Invariant Variables < ˙ E >
- Page 55 and 56: Gauge Invariant Variables < ˙ E3PN
- Page 57 and 58: Hereditary Contributions F 3PN tail
- Page 59 and 60: Log terms in total energy flux Summ
- Page 61 and 62: Log terms in total energy flux FZ t
- Page 63 and 64: Complete 3PN energy flux - Mhar <
- Page 65 and 66: Complete 3PN energy flux - Mhar <
- Page 67 and 68: Present Work Extends the circular o
- Page 69 and 70: Angular Momentum Flux Hereditary co
- Page 71 and 72: Far Zone Angular Momentum Flux dJi
- Page 73 and 74: Far Zone Angular Momentum Flux dJi
- Page 75 and 76: 3PN AMFlux - Shar dJi dt dJi dt
- Page 77 and 78: Orbital Averaged AMF - ADM Using th
3PN Mass Quadrupole for ICB<br />
where<br />
Iij = ν m<br />
<br />
+2<br />
A = 1 + 1<br />
c 2<br />
A − 24<br />
7<br />
<br />
C<br />
<br />
v 2<br />
ν<br />
c 5<br />
r ˙r 24<br />
+<br />
c2 7<br />
29<br />
G 2 m 2<br />
r 2<br />
ν<br />
c 5<br />
− 29 ν<br />
14<br />
+<br />
42 1<br />
B =<br />
1<br />
(· · ·) + (· · ·)<br />
c4 c6 11 11 1<br />
− ν +<br />
21 7 c2 <br />
Gm<br />
r<br />
+ v 2<br />
<br />
41 337<br />
−<br />
126 126<br />
+<br />
1<br />
C =<br />
1<br />
(· · ·) + (· · ·)<br />
c4 c6 − 2 6 1<br />
+ ν +<br />
7 7 c2 <br />
v 2<br />
+ G m<br />
<br />
−<br />
r<br />
155<br />
108<br />
˙r<br />
<br />
G 2 m 2<br />
<br />
r<br />
+ G m<br />
106<br />
x 〈ixj〉 + B r2<br />
c2 v 〈ivj〉 <br />
r<br />
x 〈iv j〉<br />
<br />
− 5<br />
7<br />
<br />
,<br />
+ 8<br />
7 ν<br />
<br />
335 985<br />
− ν −<br />
27 189 189 ν2<br />
733<br />
ν +<br />
126 ν2<br />
<br />
+ ˙r 2<br />
<br />
5 25<br />
−<br />
63 63<br />
+ 4057<br />
756<br />
<br />
− 13<br />
63<br />
+ 101<br />
63<br />
ν + 209<br />
108 ν2<br />
209<br />
ν −<br />
63 ν2<br />
<br />
<br />
<br />
+ 1<br />
(· · ·)<br />
c4 25<br />
ν +<br />
63 ν2<br />
<br />
BRI-IHP06-I – p.27/??
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