In 1977 Detweiler [76] discussed the resonant oscillations of a rotating black hole,
and after identifying the QNMs as ``resonance peaks'' in the
emitted spectrum he showed that the modes formally correspond to
poles of a Green function to the inhomogeneous Teukolsky
equation [197]. This idea has been extended in a more mathematically rigorous
way by Leaver [136]. Leaver extracts the QNM contribution to the emitted radiation
as a sum over residues. This sum arises when the inversion
contour of the Laplace transform, which was used to separate the
dependence on the spatial variables from the time dependence, is
deformed analytically in the complex frequency plane. In this way
the contribution from the QNM can be accounted for. Sun and
Price [194,
195] discussed in detail the way that QNM are excited by given
Cauchy data based to some extent on numerical results obtained by
Leaver [136]. Lately, Andersson [12] used the phase-integral method to determine some
characteristics of the QNM excitation.
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Quasi-Normal Modes of Stars and Black Holes
Kostas D. Kokkotas and Bernd G. Schmidt http://www.livingreviews.org/lrr-1999-2 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |