Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions

Details Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions Analytic Solutions of the Teukolsky Equation and their Low Frequency Expansions

1996-03-13

arxiv.org/abs/gr-qc/9603020v3

Prog.Theor.Phys. 95 (1996) 1079-1096

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, minor modifications

Scientific paper

10.1143/PTP.95.1079

Analytic solutions of the Teukolsky equation in Kerr geometries are presented in the form of series of hypergeometric functions and Coulomb wave functions. Relations between these solutions are established. The solutions provide a very powerful method not only for examining the general properties of solutions and physical quantities when they are applied to, but also for numerical computations. The solutions are given in the expansion of a small parameter $\epsilon \equiv 2M\omega$, $M$ being the mass of black hole, which corresponds to Post-Minkowski expansion by $G$ and to post-Newtonian expansion when they are applied 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 the theoretical template towards LIGO and VIRGO projects.

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