A stabilization procedure for the differential equations of the symmetric gyroscope including perturbing torques

Baumgarte, J.; Grünhagen, W. von

doi:10.1007/bf01230235

Cited by 4 publications

(3 citation statements)

References 3 publications

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“…It is therefore necessary, at the present time, to use results from post-Newtonian (PN) theory to extend the waveforms obtained from numerical relativity (NR). The issue of matching NR and PN waveforms for equal-mass binary blackhole systems, and using the numerical-relativity results in gravitational-wave searches, has been considered previously [17][18][19][20]. We generalize this to unequal-mass systems and suggest a phenomenological template bank parametrized only by the masses of the two individual black holes.…”

Section: Introductionmentioning

confidence: 99%

A phenomenological template family for black-hole coalescence waveforms

Ajith

Babak

Chen

et al. 2007

Class. Quantum Grav.

292

319

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Recent progress in numerical relativity has enabled us to model the nonperturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger and ring-down stages of black-hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to highermass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.

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Section: Introductionmentioning

confidence: 99%

A phenomenological template family for black-hole coalescence waveforms

Ajith

Babak

Chen

et al. 2007

Class. Quantum Grav.

292

319

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“…An early analytical estimate was made by Clark and Eardley [3] using the first post-Newtonian (1PN) Hamiltonian. Some authors [4][5][6] tried to use initial value formalisms to locate the LSO. However, the initial value approaches used in these works assume a conformally flat metric, and therefore do not correctly incorporate the well known second post-Newtonian (2PN) dynamics [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation

2000

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We discuss the analytical determination of the location of the last stable orbit ͑LSO͒ in circular general relativistic orbits of two point masses. We deal with the problem of the slow convergence of post-Newtonian expansions by ''resumming'' them in various ways. We use several different resummation methods ͑including new ones͒ based on the consideration of gauge-invariant functions, and compare the results they give at the third post-Newtonian ͑3PN͒ approximation of general relativity. Our treatment is based on the 3PN Hamiltonian of Jaranowski and Schäfer. One of the new methods we introduce is based on the consideration of the ͑invariant͒ function linking the angular momentum and the angular frequency. We also generalize the ''effective one-body'' approach of Buonanno and Damour by introducing a non-minimal ͑i.e. ''non-geodesic''͒ effective dynamics at the 3PN level. We find that the location of the LSO sensitively depends on the ͑currently unknown͒ value of the dimensionless quantity static which parametrizes a certain regularization ambiguity of the 3PN dynamics. We find, however, that all the analytical methods we use numerically agree among themselves if the value of this parameter is static ӍϪ9. This suggests that the correct value of static is near Ϫ9 ͓the precise value static * ϵϪ47/3ϩ(41/64) 2 ϭϪ9.3439 . . . seems to play a special role͔. If this is the case, we then show how to further improve the analytical determination of various LSO quantities by using a ''Shanks'' transformation to accelerate the convergence of the successive ͑already resummed͒ PN estimates.

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“…Following remarkable breakthroughs in the simulation of the strongest expected GW sources, the inspiral and coalescence of black hole binaries [3][4][5], several groups have now explored various aspects of this problem, including spin-precession and spin-flips [6,7], comparisons of numerical results with post-Newtonian (PN) predictions [8][9][10][11], multipolar analyses of the emitted radiation [8,9,12] and the use of numerical waveforms in data analysis [13][14][15][16].…”

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confidence: 99%

Multipolar analysis of spinning binaries

Berti

Cardoso

González

et al. 2008

Class. Quantum Grav.

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We present a preliminary study of the multipolar structure of gravitational radiation from spinning black hole binary mergers. We consider three different spinning binary configurations: (1) one "hang-up" run, where the black holes have equal masses and large spins initially aligned with the orbital angular momentum; (2) seven "spin-flip" runs, where the holes have a mass ratio q ≡ M 1 /M 2 = 4, the spins are anti-aligned with the orbital angular momentum, and the initial Kerr parameters of the holes j 1 = j 2 = j i (where j ≡ J/M 2 ) are fine-tuned to produce a Schwarzschild remnant after merger; (3) three "superkick" runs where the mass ratio q = 1, 2, 4 and the spins of the two holes are initially located on the orbital plane, pointing in opposite directions. For all of these simulations we compute the multipolar energy distribution and the Kerr parameter of the final hole. For the hang-up run, we show that including leading-order spin-orbit and spin-spin terms in a multipolar decomposition of the post-Newtonian waveforms improves agreement with the numerical simulation.These are exciting times for gravitational wave (GW) research. Earth-based laserinterferometric detectors are collecting data at design sensitivity, and LIGO [1] just completed the longest scientific run to date. The space-based interferometer LISA is expected to open an observational window at low frequencies (∼ 10 −4 − 10 −1 Hz) within the next decade [2]. Following remarkable breakthroughs in the simulation of the strongest expected GW sources, the inspiral and coalescence of black hole binaries [3,4,5], several groups have now explored various aspects of this problem, including spin-precession and spin-flips [6,7], comparisons of numerical results with post-Newtonian (PN) predictions [8,9,10,11], multipolar analyses of the emitted radiation [8,9,12] and the use of numerical waveforms in data analysis [13,14,15,16].In Ref.[9] we studied the multipolar distribution of radiation and the final spin resulting from the merger of unequal-mass, non-spinning black holes with mass ratios q = M 1 /M 2 in the range 1 to 4. The main purpose of this paper is to show preliminary results from our attempt to extend the analysis to spinning binaries.

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A stabilization procedure for the differential equations of the symmetric gyroscope including perturbing torques

Cited by 4 publications

References 3 publications

A phenomenological template family for black-hole coalescence waveforms

A phenomenological template family for black-hole coalescence waveforms

Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation

Multipolar analysis of spinning binaries

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