Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
3.5PN accurate reactive dynamics Explicit computations of RHS require only 1PN accurate expressions for the orbital elements because we are trying to obtain the phasing to the 3.5PN order and the reactive dynamics only involves 2.5PN and 3.5PN contributions. BUT, this does not mean that the orbital dynamics is only 1PN accurate. Phasing formalism allows us to impose the fully 1PN accurate reactive dynamics on the 3PN accurate conservative dynamics to provide the 3.5PN accurate phasing BRI-IHP06-I – p.128/??
3.5PN accurate reactive dynamics Finally, the evolution equations for dn/dl, det/dl, dcl/dl, and dcλ/dl in terms of u(l, n, et), n, and et, dn dl = − 8ξ5/3nη 5 6 32 − χ3 ξ7/3 nη −360 + 1176η 35 χ 3 χ4 + 49 − 9e2 t χ5 + 2680 − 11704η − 35(1 − e2 t ) χ6 − − 4012 + 34356η + (36 − 756η)e 2 t χ 4 1470 − 47880η − (350 − 17080η)e 2 t 1 + χ5 1 + χ6 13510 + 31780η − (24220 + 30520η)e 2 t + (10710 − 1260η)e 4 t (27594 + 5880η)(1 − e 2 t )2 χ 8 χ ≡ 1 − et cos u and u = u(l, n, et). + + 11760(1 − e2 t )3 χ 9 , 1 − χ7 BRI-IHP06-I – p.129/??
- 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 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: 3.5PN accurate reactive dynamics A
- 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
3.5PN accurate reactive dynamics<br />
Explicit computations of RHS require only 1PN accurate expressions<br />
for the orbital elements because we are try<strong>in</strong>g to obta<strong>in</strong> the phas<strong>in</strong>g<br />
to the 3.5PN order and the reactive dynamics only <strong>in</strong>volves 2.5PN<br />
and 3.5PN contributions.<br />
BUT, this does not mean that the orbital dynamics is only 1PN<br />
accurate. Phas<strong>in</strong>g formalism allows us to impose the fully 1PN<br />
accurate reactive dynamics on the 3PN accurate conservative<br />
dynamics to provide the 3.5PN accurate phas<strong>in</strong>g<br />
BRI-IHP06-I – p.128/??
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