Key points are not available for this paper at this time.
The angular dependence of the gravitational radiation emitted in compact binary mergers and gravitational collapse is usually separated using spin-weighted spherical harmonics ₒY_ of spin weight s, that reduce to the ordinary spherical harmonics Y_ when s=0. Teukolsky first showed that the perturbations of the Kerr black hole that may be produced as a result of these events are separable in terms of a different set of angular functions: the spin-weighted spheroidal harmonics ₒS_, where n denotes the ``overtone index'' of the corresponding Kerr quasinormal mode frequency _. In this paper we compute the complex-valued scalar products of the ₒS_'s with the ₒY_'s (``spherical-spheroidal mixing coefficients'') and with themselves (``spheroidal-spheroidal mixing coefficients'') as functions of the dimensionless Kerr parameter j. Tables of these coefficients and analytical fits of their dependence on j are available online for use in gravitational-wave source modeling and in other applications of black-hole perturbation theory.
Berti et al. (Mon,) studied this question.