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 generalised Quasi-Keplerian reprn r = ar (1 − er cos u) , l ≡ n (t − t0) = u − et sin u + f4t + c4 f6t + c6 2 π Φ (φ − φ0) = V + f4φ f6φ + c4 c6 + i6φ h6φ sin 4V + c6 1 + eφ where, V = 2 arctan 1 − eφ Details: Schäfer’s Lectures g4t g6t + c4 c6 sin V + i6t c sin 2V + c 6 sin 5V , 1/2 (V − u) 6 sin 2 V + h6t tan u 2 g4φ g6φ + c4 c6 . sin 3 V , c6 sin 3V BRI-IHP06-I – p.37/??
3PN generalised Quasi-Keplerian reprn V is the 3PN generalisation of the Keplerian true anomaly. ar, er, l, u, n, et, eφ and 2π/Φ are some 3PN accurate semi-major axis, radial eccentricity, mean anomaly, eccentric anomaly, mean motion, ‘time’ eccentricity, angular eccentricity and angle of advance of periastron per orbital revolution respectively. Eqns contain three kinds of ‘eccentricities’ et, er and eφ labelled after the coordinates t, r, and φ respectively. Differ from each other starting at the 1PN order. Φ/2π ≡ K = 1 + k Presense of log terms in Std Harmonic coords obstructs the construction of GQKR which crucially exploits the fact that at order 3PN the radial equation is a fourth order polynomial in 1/r. MGS04 thus construct the GQKR for Modified Harmonic coords. GQKR in Modified Harmonic coords is of the same form as for ADM but the corresponding eqns for the orbital elements are different. BRI-IHP06-I – p.38/??
- 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
- Page 17 and 18: 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
- Page 29 and 30: Instantaneous Terms dE dt inst d
- Page 31 and 32: 3PN Instantaneous Terms dE dt 2PN
- Page 33 and 34: Transfn of World lines Having obtai
- Page 35 and 36: Energy Flux - Modified Harmonic Coo
- Page 37: 3PN generalised Quasi-Keplerian rep
- Page 41 and 42: 3PN GQKR - Mhar n = (−2E) 3/2 +11
- 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
3PN generalised Quasi-Keplerian reprn<br />
V is the 3PN generalisation of the Keplerian true anomaly.<br />
ar, er, l, u, n, et, eφ and 2π/Φ are some 3PN accurate semi-major<br />
axis, radial eccentricity, mean anomaly, eccentric anomaly, mean<br />
motion, ‘time’ eccentricity, angular eccentricity and angle of<br />
advance of periastron per orbital revolution respectively.<br />
Eqns conta<strong>in</strong> three k<strong>in</strong>ds of ‘eccentricities’ et, er and eφ labelled<br />
after the coord<strong>in</strong>ates t, r, and φ respectively. Differ <strong>from</strong> each other<br />
start<strong>in</strong>g at the 1PN order.<br />
Φ/2π ≡ K = 1 + k<br />
Presense of log terms <strong>in</strong> Std Harmonic coords obstructs the<br />
construction of GQKR which crucially exploits the fact that at order<br />
3PN the radial equation is a fourth order polynomial <strong>in</strong> 1/r.<br />
MGS04 thus construct the GQKR for Modified Harmonic coords.<br />
GQKR <strong>in</strong> Modified Harmonic coords is of the same form as for ADM<br />
but the correspond<strong>in</strong>g eqns for the orbital elements are different.<br />
BRI-IHP06-I – p.38/??
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