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Prog. Theor. Phys. Vol. 96 No. 3 (1996) pp. 549-565

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

Shuhei Mano, Hisao Suzuki^* and Eiichi Takasugi

Department of Physics, Osaka University, Toyonaka 560
^*Department of Physics, Hokkaido University, Sapporo 060

(Received June 11, 1996)

Abstract:

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

URL : http://ptp.ipap.jp/link?PTP/96/549/
DOI : 10.1143/PTP.96.549

[ Full Text PDF : FREE ACCESS (629K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. S. Mano, H. Suzuki and E. Takasugi, Osaka University Preprint, OU-HET 237.
   S. Mano, Soryusiron Kenkyu (Kyoto), 92 (1995), C166.
2. E. W. Leaver, J. Math. Phys. 27 (1986), 1238[CrossRef].
3. S. A. Teukolsky, Astrophys. J. 185 (1973), 635[CrossRef].
4. V. S. Otchik, in Quantum Systems: New Trends and Methods., ed. A. O. Barut et al. (World Scientific, 1995), p. 154.
5. S. Mano, H. Suzuki and E. Takasugi, Prog. Theor. Phys. 95 (1996), 1079[PTP].
6. E. Poisson and M. Sasaki, Phys. Rev. D51 (1995), 5753[APS].
7. See, for example, H. Tagoshi and T. Nakamura, Phys. Rev. D49 (1994), 4016[APS].
8. A. Erdelyi et al., Higher Transcendental equation, Vol. 1 (McGraw-Hill, 1953).

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 97 No. 2 (1997) pp. 213-232 :

   Analytic Solutions of the Teukolsky Equation and Their Properties

   Shuhei Mano and Eiichi Takasugi

2. Progress of Theoretical Physics Vol. 102 No. 2 (1999) pp. 253-272 :

   Analytic Solutions of the Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

   Hisao Suzuki, Eiichi Takasugi and Hiroshi Umetsu

3. Progress of Theoretical Physics Vol. 103 No. 4 (2000) pp. 723-731 :

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4. Progress of Theoretical Physics Vol. 111 No. 6 (2004) pp. 821-840 :

   A New Analytical Method for Self-Force Regularization. I

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5. Progress of Theoretical Physics Vol. 113 No. 2 (2005) pp. 283-303 :

   A New Analytical Method for Self-Force Regularization. II

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6. Progress of Theoretical Physics Supplement No.128 (1997) pp. 1-121 :

   Chapter 1. Black Hole Perturbation

   Yasushi Mino, Misao Sasaki, Masaru Shibata, Hideyuki Tagoshi and Takahiro Tanaka

7. Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145 :

   Gravitational Radiation Reaction

   Takahiro Tanaka

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