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Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion

Shuhei Mano·Hisao Suzuki·Eiichi Takasugi
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Abstract

Analytic solutions of the Regge-Wheeler equation are presented in the form of series of hypergeometric functions and Coulomb wave functions which have different regions of convergence. Relations between these solutions are established. The series solutions are given as the Post-Minkowskian expansion with respect to a parameter $ε\equiv 2Mω$, $M$ being the mass of black hole. This expansion corresponds to the post-Newtonian expansion when they are applied to the gravitational radiation from a particle in circular orbit around a black hole. These solutions can also be useful for numerical computations.

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Shuhei Mano, Hisao Suzuki, Eiichi Takasugi. 1996-05-27. Analytic Solutions of the Regge-Wheeler Equation and the Post-Minkowskian Expansion. https://doi.org/10.1143/ptp.96.549

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