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 accurate conservative dynamics −2EL 2 = ξ ≡ GMn/c 3 1 + ξ2/3 4(1 − e 2 t ) 9 + η − (17 − 7η)e 2 t + ξ 4/3 24(1 − e 2 t )2 189 − 45η + η 2 − 2(111 + 7η + 15η 2 )e 2 t + (225 − 277η + 29η2 )e 4 t − (360 − 144η)e2 t ξ 2 6720(1 − e 2 t )3 35(5535 − 9061η + 246π 2 η + 142η 2 − η 3 ) + (299145 − 1197667η + 25830π 2 η + 173250η 2 + 2345η 3 )e 2 t + 1 − e 2 t 35(3549 − 12783η + 6154η 2 − 131η 3 )e 4 t − 35(2271 − 7381η + 2414η2 − 65η 3 70 24(45 − 13η − 2η 2 ) − (17880 − 20120η +123π 2 η + 2256η 2 )e 2 t + 96(55 − 40η + 3η 2 )e 4 t 1 − e2 t (1 − e 2 t ) , BRI-IHP06-I – p.118/??
3PN accurate conservative dynamics To compute expressions for ˙r and ˙ φ, need the following relations: ∂S ∂l = arer sin u ∂u ∂l , ∂W ∂l ∂u ∂l = = 1 + k + 2 f4φ f6φ + c4 c6 cos 2v + 3 5 h6φ ∂v ∂u cos 5v − (1 + k) , c6 ∂u ∂l 1 − et cos u − g4t c 3 h6t −1 ∂v cos 3v , c6 ∂u ∂v ∂u = (1 − e2 φ )1/2 1 − eφ cos u . g4φ g6φ + c4 c6 g6t g4t g6t f4t − + + + 4 6 4 6 c c c f6t + c4 c6 cos 3v + 4 i6φ cos 4v+ c6 cos v + 2 i6t cos 2v c6 BRI-IHP06-I – p.119/??
- 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
- 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: 3PN accurate conservative dynamics
- Page 123 and 124: 3PN accurate conservative dynamics
- Page 125 and 126: 3PN accurate conservative dynamics
- Page 127 and 128: 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
3PN accurate conservative dynamics<br />
To compute expressions for ˙r and ˙ φ, need the follow<strong>in</strong>g relations:<br />
∂S<br />
∂l = arer s<strong>in</strong> u ∂u<br />
∂l ,<br />
∂W<br />
∂l<br />
∂u<br />
∂l<br />
=<br />
=<br />
<br />
1 + k + 2<br />
<br />
f4φ f6φ<br />
+<br />
c4 c6 <br />
cos 2v + 3<br />
5 h6φ<br />
<br />
∂v ∂u<br />
cos 5v − (1 + k) ,<br />
c6 ∂u ∂l<br />
<br />
1 − et cos u − g4t<br />
c<br />
3 h6t<br />
−1 ∂v<br />
cos 3v ,<br />
c6 ∂u<br />
∂v<br />
∂u = (1 − e2 φ )1/2<br />
1 − eφ cos u .<br />
g4φ<br />
g6φ<br />
+<br />
c4 c6 <br />
g6t g4t g6t f4t<br />
− + + +<br />
4 6 4 6<br />
c<br />
c<br />
c<br />
<br />
f6t<br />
+<br />
c4 c6 cos 3v + 4 i6φ<br />
cos 4v+<br />
c6 <br />
cos v + 2 i6t<br />
cos 2v<br />
c6 BRI-IHP06-I – p.119/??
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