ANALYTIC SOLUTIONS OF THE TEUKOLSKY EQUATION AND THEIR LOW-FREQUENCY EXPANSIONS

Analytic solutions of the Teukolsky equation for arbitrary spin weight in Kerr geometry are presented in the form of series of hypergeometri c functions and Coulomb wave functions. Relations between these soluti ons are established. The solutions provide a very powerful method not only for examining the general properties of solutions and physical qu antities both analytically and numerically. The solutions can be regar ded as series expansions in terms of a small parameter epsilon = 2M om ega, M being the mass of black hole, which corresponds to the Post-Min kowski expansion by G and to post-Newtonian expansion when they are ap plied to the gravitational radiation from a particle in circular orbit around a black hole. It is expected that these solutions will become a powerful weapon to construct accurate theoretical templates for LIGO and VIRGO projects.