Analytic Solutions of the Teukolsky Equation and their Properties

Details Analytic Solutions of the Teukolsky Equation and their Properties Analytic Solutions of the Teukolsky Equation and their Properties

1996-11-06

arxiv.org/abs/gr-qc/9611014v1

Prog.Theor.Phys. 97 (1997) 213-232

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages

Scientific paper

10.1143/PTP.97.213

The analytical solutions reported in our previous paper are given as series of hypergeometric or Coulomb wave functions. By using them, we can get the Teukolsky functions analytically in a desired accuracy. For the computation, the deep understanding of their properties is necessary. We summarize the main result: The relative normalization between the solutions with a spin weight s and -s is given analytically by using the Teukolsky-Starobinsky (T-S) identities. By examining the asymptotic behaviors of our solution and combined with the T-S identities and the Wronskian, we found nontrivial identities between the sums of coefficients of the series. These identities will serve to make various expression in simpler forms and also become a powerful tool to test the accuracy of the computation. As an application, we investigated the absorption rate and the evaporation rate of black hole and obtain interesting analytic results.

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