Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Evoln of orbital elements under GRR The three expressions obtained here are the 3PN generalizations of the expressions given in Peters which are at the lowest quadrupolar order. They could be used to provide 3PN extensions of n(e) and a(e) relations in the future. The above results have to be supplemented by the computation of hereditary terms at 2.5PN and 3PN for completion. These hereditary terms include the tails at 2.5PN and tail of tails and tail-square terms at 3PN. Formally one can analytically solve the coupled evolution system by successive approximations, reducing it to simple quadratures. Eg, at the leading order O(c −5 ) one can first eliminate t by dividing d¯n/dt by dēt/dt, thereby obtaining an equation of the form d ln ¯n = f0(ēt)dēt. Integration of this equation yields ¯n(ēt) = ni e 18/19 i (304 + 121 e 2 i ) 1305/2299 (1 − e 2 i )3/2 e 18/19 t (1 − e 2 t ) 3/2 (304 + 121 e2 , t ) 1305/2299 ei is the value of et when n = ni. First obtained by Peters 64. BRI-IHP06-I – p.93/??
PART II Based on Phasing of Gravitational waves fluxes from inspiralling eccentric binaries 2.5PN/3.5PN T. Damour, A. Gopakumar and B. R. Iyer Phys.Rev. D70 (2004) 064028 C. Koenigsdoerffer, A. Gopakumar Phys.Rev. D73 (2006) 124012
- Page 43 and 44: 3PN GQKR - Mhar + Φ = 2 π 70 16
- Page 45 and 46: Orbital average - Energy flux -MHar
- Page 47 and 48: Orbit Averaged Energy Flux - MHar <
- Page 49 and 50: Comments Note: No term at 2.5PN. 2.
- 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: Evoln of orbital element ar under G
- 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 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
PART II<br />
Based on<br />
Phas<strong>in</strong>g of <strong>Gravitational</strong> waves fluxes <strong>from</strong> <strong>in</strong>spirall<strong>in</strong>g<br />
eccentric b<strong>in</strong>aries 2.5PN/3.5PN<br />
T. Damour, A. Gopakumar and B. R. Iyer<br />
Phys.Rev. D70 (2004) 064028<br />
C. Koenigsdoerffer, A. Gopakumar<br />
Phys.Rev. D73 (2006) 124012
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