ANALYTIC SOLUTIONS OF THE TEUKOLSKY EQUATION AND THEIR PROPERTIES

The analytical solutions reported in our previous paper are given as s eries of hypergeometric or Coulomb wave functions. Using them, we can get the Teukolsky functions analytically in a desired accuracy. For th e 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 using the Teukolsky-Starobinsky (T-S) identities. By examining the asymptotic b ehavior of our solution and combined with the T-S identities and the W ronskian, we found nontrivial identities between the sums of coefficie nts of the series. These identities will serve to make various express ion in simpler forms and also become a powerful tool to test the accur acy of the computation. As an application, we investigated the absorpt ion rate and the evaporation rate of black hole and obtain interesting analytic results.