Uniformly valid asymptotic expansions are derived, both in the high-frequency and the low-frequency limits, for the solution of Zerilli's equation for even-parity gravitational perturbations on the Schwarzschild geometry. The high-frequency solutions should prove useful in the analysis of bursts of gravitational radiation, which are emitted during nonspherical gravitational collapse and also during the infall of a particle into a black hole. The low4requency solutions govern the decay with time of the gravitational-multipole moments of a newly formed, slightly nonspherical, black hole.
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Edward D. Fackerell (1971) studied this question.