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

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

1996-05-27

arxiv.org/abs/gr-qc/9605057v1

Prog.Theor.Phys. 96 (1996) 549-566

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages

Scientific paper

10.1143/PTP.96.549

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 $\epsilon \equiv 2M\omega$, $M$ 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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