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O. W. Day Jr. (Dept. of Physics, East Carolina University), D. W. Pravica (Dept. of Mathematics, East Carolina University)
The complex scaling method is applied to the General Relativistic wave equation in the region outside and surrounding a black hole, for gravitational and for electromagnetic oscillations. We discuss the resultant resonant frequencies and states. The imaginary part of the frequency spectrum gives inverse lifetimes to resonant phenomena. This model is able to explain various aspects of the QPO spectrum in the x-ray emission, including: (a) the 3:2 ratio between the real parts of the two highest frequencies. (b) the frequency dependence on 1/M, where M is the mass of the black hole. (c) the variability in the frequencies and ratios, which may change by several percent during a flaring event. (d) the region where the resonant state may appear and the sensitivity to perturbations for its creation. (e) an asymptotic value in the ratio of any two frequencies in the spectrum, which occurs when the density of plasma becomes small in the region of oscillations. Some similarity with the spectrum of several Extremely Low Frequency (ELF), global, “Schumann” resonances in the electromagnetic field surrounding Earth is noted. Also discussed is the application of the theory to quark stars. Theoretical and experimental values for frequencies and masses are compared for three black holes with the greatest number of measured spectral components: XTE J1550-564, GRO J1655-40 and GRS 1915+105.
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The author(s) of this abstract have provided an email address for comments about the abstract: pravicad@mail.ecu.edu
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Bulletin of the American Astronomical Society, 36 #3
© 2004. The American Astronomical Soceity.