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

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3PN accurate conservative dynamics ˙φ = ˙ φN + ˙ φ1PN + ˙ φ2PN + ˙ φ3PN , ˙φN = n ˙φ1PN = ˙ φN × ˙φ2PN = ˙ φN × ˙φ3PN = ˙ φN × 1 − e 2 t , (1 − et cos u) 2 ξ 2/3 (1 − e 2 t )(1 − et cos u) ξ 4/3 12(1 − e 2 t )2 (1 − et cos u) 3 ξ 2 (1 − e 2 t )3 (1 − et cos u) 5 3 − (4 − η)e 2 t + (1 − η)et cos u , · · · · · · · · · · · · · · BRI-IHP06-I – p.124/??
3PN accurate conservative dynamics Eccentric anomaly u = U(l, n, et) given by inverting the 3PN accurate Kepler equation, connecting l and u. l = u − et sin u + + 8 ξ4/3 1 − e2 t (1 − et cos u) ξ 2 6720(1 − e 2 t )3/2 (1 − et cos u) 3 (15η − η 2 )et sin u 1 − e2 t + 12(5 − 2η)(v − u)(1 − et c 67200 + 143868η − 4305π 2 η − 62160η 2 − 280η (134400 + 139896η − 8610π 2 η − 67200η 2 − 3920η 3 )et cos u +(67200 − 752η − 4305π 2 η − 15260η 2 − 1820η 3 )(et cos u) 2 + −148960η + 45500η 2 − 1540η 3 + (143640η − 13440η 2 − 3920η 3 )et cos u −(1120η + 11620η 2 − 1820η 3 ) ×(et cos u) 2 e 2 t + (3220η − 10220η2 + 1820η 3 )e 4 t ×et sin u 1 − e2 t + 302400 − 461440η + 4305π 2 η + 33600η 2 + i (100800 − 97440η + 36960η 2 )e 2 t (v − u)(1 − et cos u) 3 No 1PN contribution, in ADM or modified harmonic coords. Expected differences in the Kepler equation at higher-PN orders between the harmonic BRI-IHP06-I – p.125/?? .
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
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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
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Instantaneous Terms dE dt inst d
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3PN Instantaneous Terms dE dt 2PN
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Transfn of World lines Having obtai
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Energy Flux - Modified Harmonic Coo
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3PN generalised Quasi-Keplerian rep
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3PN generalised Quasi-Keplerian rep
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3PN GQKR - Mhar n = (−2E) 3/2 +11
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3PN GQKR - Mhar + Φ = 2 π 70 16
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Orbital average - Energy flux -MHar
Page 47 and 48:
Orbit Averaged Energy Flux - MHar <
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Comments Note: No term at 2.5PN. 2.
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Comments Useful internal consistenc
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Gauge Invariant Variables < ˙ E >
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Gauge Invariant Variables < ˙ E3PN
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Hereditary Contributions F 3PN tail
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Log terms in total energy flux Summ
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Log terms in total energy flux FZ t
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Complete 3PN energy flux - Mhar <
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Complete 3PN energy flux - Mhar <
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Present Work Extends the circular o
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Angular Momentum Flux Hereditary co
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Far Zone Angular Momentum Flux dJi
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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
Page 99 and 100: Phasing of GWF TT radn field is giv
Page 101 and 102: Phasing of GWF Orbital phase = φ,
Page 103 and 104: Method of variation of constants A
Page 105 and 106: Method of variation of constants c1
Page 107 and 108: Method of variation of constants At
Page 109 and 110: Method of variation of constants An
Page 111 and 112: Method of variation of constants Al
Page 113 and 114: Method of variation of constants Fo
Page 115 and 116: Method of variation of constants Du
Page 117 and 118: Implementation Compute 3PN accurate
Page 119 and 120: 3PN accurate conservative dynamics
Page 125: 3PN accurate conservative dynamics
Page 129 and 130: 3.5PN accurate reactive dynamics A
Page 131 and 132: 3.5PN accurate reactive dynamics Fi
Page 133 and 134: 3.5PN accurate reactive dynamics dc
Page 135 and 136: 3.5PN accurate reactive dynamics 4
Page 137 and 138: Secular variations d¯n dt dēt dt
Page 139 and 140: Periodic variations To complete thi
Page 141 and 142: Periodic variations One can analyti
Page 143 and 144: Periodic variations ˜cl = − 2ξ5
Page 145 and 146: Periodic variations Above results m
Page 147 and 148: Periodic variations ˜ l(l; ¯ca) =
Page 149 and 150: ¯n/ni and ñ/n versus l/(2π) n /
Page 151 and 152: h+(t) and h×(t) Scaled h + (t) Sca
Page 153 and 154: ¯n/ni and ñ/n ēt and ˜et versus
Page 155 and 156: ¯cl and ˜cl ¯cλ and ˜cλ versu
Page 157 and 158: Validity of Results Circular orbits
Page 159: References 1. P. C. Peters, Phys. R
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Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

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