Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Orbit Averaged Energy Flux - MHar < ˙ E3PN >Mhar = 1 1 − e 2 t 3 (· · · · · ·) BRI-IHP06-I – p.47/??
Comments Note: No term at 2.5PN. 2.5PN contribution is proportional to ˙r and vanishes after averaging since it always includes only ‘odd’ terms. et represents eccentricity in Modified harmonic coordinates e MHar t . x is gauge invariant. No such label is required on it. Important to keep track when comparing formulas in different gauges. Circular orbit limit - setting et = 0, < ˙ E > |⊙ = 32 5 x5 ν 2 x 3 1 + x 1266161801 9979200 − 1247 − 94403 3024 ν2 − 775 324 ν3 35 − 336 12 ν + x 2 − 44711 9072 1712 − 105 ln Gm c2 + − xr0 14930989 272160 9271 65 + ν + 504 18 ν2 Exact agreement with BIJ02 after converting the γ = Gm/c 2 rSHar to the gauge invariant variable x. This is only instantaneous contribution . 41 + 48 π2 − 88 3 BRI-IHP06-I – p.48/??
- 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 and 28: 3PN EOM for ICB a i = dvi dt AE = 1
- Page 29 and 30: Instantaneous Terms dE dt inst d
- 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: Orbit Averaged Energy Flux - MHar <
- 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
- Page 79 and 80: Orbital Averaged AMF - ADM 〈 dJ d
- Page 81 and 82: Orbital Averaged AMF - ADM 〈 dJ d
- Page 83 and 84: Evoln of orbital elements under GRR
- Page 85 and 86: Evoln of orbital element n under GR
- Page 87 and 88: Evoln of orbital element n under GR
- Page 89 and 90: Evoln of orbital element et under G
- Page 91 and 92: Evoln of orbital element ar under G
- Page 93 and 94: Evoln of orbital element ar under G
- Page 95 and 96: PART II Based on Phasing of Gravita
- Page 97 and 98: Beyond Orbital Averages Going beyon
Comments<br />
Note: No term at 2.5PN. 2.5PN contribution is proportional to ˙r and<br />
vanishes after averag<strong>in</strong>g s<strong>in</strong>ce it always <strong>in</strong>cludes only ‘odd’ terms.<br />
et represents eccentricity <strong>in</strong> Modified harmonic coord<strong>in</strong>ates e MHar<br />
t .<br />
x is gauge <strong>in</strong>variant. No such label is required on it.<br />
Important to keep track when compar<strong>in</strong>g formulas <strong>in</strong> different<br />
gauges.<br />
Circular orbit limit - sett<strong>in</strong>g et = 0,<br />
< ˙<br />
E > |⊙ = 32<br />
5 x5 ν 2<br />
x 3<br />
<br />
1 + x<br />
1266161801<br />
9979200<br />
<br />
− 1247<br />
− 94403<br />
3024 ν2 − 775<br />
324 ν3<br />
<br />
35<br />
−<br />
336 12 ν + x 2<br />
− 44711<br />
9072<br />
1712<br />
−<br />
105 ln<br />
<br />
Gm<br />
c2 <br />
+ −<br />
xr0<br />
14930989<br />
272160<br />
<br />
9271 65<br />
+ ν +<br />
504 18 ν2<br />
Exact agreement with BIJ02 after convert<strong>in</strong>g the γ = Gm/c 2 rSHar to<br />
the gauge <strong>in</strong>variant variable x.<br />
<br />
This is only <strong>in</strong>stantaneous contribution<br />
.<br />
41<br />
+<br />
48 π2 − 88<br />
3<br />
BRI-IHP06-I – p.48/??
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