Echeverria, Fernando (1989) Gravitationalwave measurements of the mass and angular momentum of a black hole. Physical Review D, 40 (10). pp. 31943203. ISSN 24700010. https://resolver.caltech.edu/CaltechAUTHORS:ECHprd89

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Abstract
A deformed black hole produced in a cataclysmic astrophysical event should undergo damped vibrations which emit gravitational radiation. By fitting the observed gravitational waveform h(t) to the waveform predicted for blackhole vibrations, it should be possible to deduce the hole’s mass M and dimensionless rotation parameter a=(c/G)(angular momentum)/M^2. This paper estimates the accuracy with which M and a can be determined by optimal signal processing of data from laserinterferometer gravitationalwave detectors. It is assumed that the detector noise has a white spectrum and has been made Gaussian by cross correlation of detectors at different sites. Assuming, also, that only the most slowly damped mode (which has spheroidal harmonic indices l=m=2) is significantly excited—as probably will be the case for a hole formed by the coalescence of a neutronstar binary or a blackhole binary—it is found that the onesigma uncertainties in M and a are ΔM/M≃2.2ρ^1(1a)^0.45, Δa≃5.9ρ^1(1a)^1.06, where ρ≃hs(πSh)^1/2 (1a)^0.22. Here ρ is the amplitude signaltonoise ratio at the output of the optimal filter, hs is the wave’s amplitude at the beginning of the vibrations, f is the wave’s frequency (the angular frequency ω divided by 2π), and Sh is the frequencyindependent spectral density of the detectors’ noise. These formulas for ΔM and Δa are valid only for ρ≳10. Corrections to these approximate formulas are given in Table II.
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Additional Information:  ©1989 The American Physical Society Received 27 December 1988 I wish to thank Dr. Kip S. Thorne, for suggesting this problem to me and for many suggestions that helped me with the research and in writing this paper. I am also indebted to Dr. E.W. Leaver, who supplied me with his unpublished numerical results on the frequencies and damping times of the fundamental l = m = 2 mode of Kerr black holes, which were necessary for my calculations. This work was supported in part by the National Science Foundation under Grant No. AST8514911.  
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Deposited On:  12 Dec 2006  
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