Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-07-29
Phys.Rev.D82:104003,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, 3 tables, 3 figures
Scientific paper
10.1103/PhysRevD.82.104003
It is well established that the response of a black hole to a generic perturbation is characterized by a spectrum of damped resonances, called quasinormal modes; and that, in the limit of large angular momentum ($l \gg 1$), the quasinormal mode frequency spectrum is related to the properties of unstable null orbits. In this paper we develop an expansion method to explore the link. We obtain new closed-form approximations for the lightly-damped part of the spectrum in the large-$l$ regime. We confirm that, at leading order in $l$, the resonance frequency is linked to the orbital frequency, and the resonance damping to the Lyapunov exponent, of the relevant null orbit. We go somewhat further than previous studies to establish (i) a spin-dependent correction to the frequency at order $1 / l$ for equatorial ($m = \pm l$) modes, and (ii) a new result for polar modes ($m = 0$). We validate the approach by testing the closed-form approximations against frequencies obtained numerically with Leaver's method.
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