Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Phasing of GWF h+,× expressed only in terms of r, φ and their time derivatives because restricted to non-spinning objects. In the presence of spin interactions, the orbital plane is no longer fixed in space and one needs to introduce further variables, notably a (slowly varying) ‘longitude of the node’ Ω. Correspondingly, the polarization direction p cannot be defined anymore as the line of nodes. Such a situation dealt with in the problem of the timing of binary pulsars (Damour Taylor 92) and might be advantageous to use the conventions used there to define p and q. Namely, in terms of (DT92), p = I0, q = J0. Note that the binary pulsar convention uses as the third vector I0 × J0, the direction from the observer to the source. Explicit functional forms for h+(r, φ, ˙r, ˙ φ), h×(r, φ, ˙r, ˙ φ) and phasing relations r(t), φ(t), ˙r(t) and ˙ φ(t) depend on the coordinate system used, though the final results h+(t) and h×(t) do not h T T ij and therefore h+(t) and h×(t) are coordinate independent asymptotic quantities. BRI-IHP06-I – p.100/??
Method of variation of constants A version of the general Lagrange method of variation of arbitrary constants, which was employed to compute within GR the orbital evolution of the Hulse-Taylor binary pulsar (Damour 83, 85). Begins by splitting the relative acceleration of the compact binary A into two parts: an integrable leading part A0 and a perturbation part, A ′ A = A0 + A ′ . Eg to work at 2.5PN accuracy choose A0 to be the acceleration at 2PN order and A ′ to be the c −5 RR; for 3.5PN-accurate calculation A0 would be the conservative part of the 3PN dynamics, and A ′ the O(c −5 ) + O(c −7 ) RR BRI-IHP06-I – p.101/??
- 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
- Page 99 and 100: Phasing of GWF TT radn field is giv
- Page 101: Phasing of GWF Orbital phase = φ,
- 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 121 and 122: 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
Method of variation of constants<br />
A version of the general Lagrange method of variation of<br />
arbitrary constants, which was employed to compute with<strong>in</strong><br />
GR the orbital evolution of the Hulse-Taylor b<strong>in</strong>ary pulsar<br />
(Damour 83, 85).<br />
Beg<strong>in</strong>s by splitt<strong>in</strong>g the relative acceleration of the compact<br />
b<strong>in</strong>ary A <strong>in</strong>to two parts: an <strong>in</strong>tegrable lead<strong>in</strong>g part A0 and a<br />
perturbation part, A ′<br />
A = A0 + A ′ .<br />
Eg to work at 2.5PN accuracy choose A0 to be the<br />
acceleration at 2PN order and A ′ to be the c −5 RR; for<br />
3.5PN-accurate calculation A0 would be the conservative<br />
part of the 3PN dynamics, and A ′ the O(c −5 ) + O(c −7 ) RR<br />
BRI-IHP06-I – p.101/??
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