%0 Journal Article %1 Mano1996Analytic %A Mano, Shuhei %A Takasugi, Eiichi %D 1996 %K greybodyfactors, heun-eqn %R 10.1143/PTP.97.213 %T Analytic Solutions of the Teukolsky Equation and their Properties %U http://dx.doi.org/10.1143/PTP.97.213 %X 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.

@article{Mano1996Analytic, abstract = {{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.}}, added-at = {2019-02-26T10:37:35.000+0100}, archiveprefix = {arXiv}, author = {Mano, Shuhei and Takasugi, Eiichi}, biburl = {https://www.bibsonomy.org/bibtex/2f1275c10bab9e08f04cad577d07a3f70/acastro}, citeulike-article-id = {4445533}, citeulike-linkout-0 = {http://dx.doi.org/10.1143/PTP.97.213}, citeulike-linkout-1 = {http://arxiv.org/abs/gr-qc/9611014}, citeulike-linkout-2 = {http://arxiv.org/pdf/gr-qc/9611014}, day = 6, doi = {10.1143/PTP.97.213}, eprint = {gr-qc/9611014}, interhash = {2697997d58ddd4188979ed9df3b81c4b}, intrahash = {f1275c10bab9e08f04cad577d07a3f70}, keywords = {greybodyfactors, heun-eqn}, month = nov, posted-at = {2012-06-17 18:34:18}, priority = {2}, timestamp = {2019-02-26T10:37:35.000+0100}, title = {{Analytic Solutions of the Teukolsky Equation and their Properties}}, url = {http://dx.doi.org/10.1143/PTP.97.213}, year = 1996 }