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Prog. Theor. Phys. Vol. 95 No. 6 (1996) pp. 1079-1096

[ Full Text PDF : FREE ACCESS (704K) ]

Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions

Shuhei Mano, Hisao Suzuki and Eiichi Takasugi

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

(Received March 6, 1996)

Abstract:

Analytic solutions of the Teukolsky equation for arbitrary spin weight in Kerr geometry 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 both analytically and numerically. The solutions can be regarded as series expansions in terms of a small parameter ε≡2Mω, M being the mass of black hole, which corresponds to the 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 accurate theoretical templates for LIGO and VIRGO projects.


URL : http://ptp.ipap.jp/link?PTP/95/1079/
DOI : 10.1143/PTP.95.1079

[ Full Text PDF : FREE ACCESS (704K) ] Citation:

References:

  1. S. A. Teukolsky, Astrophys. J. 185 (1973), 635[CrossRef].
  2. D. N. Page, Phys. Rev. D13 (1976), 198[APS].
  3. A. A. Starobinsky and Churilov, Sov. Phys-JETP 38 (1974), 1.
  4. E. W. Leaver, J. Math. Phys. 27 (1986), 1238[CrossRef].
  5. H. Tagoshi and T. Nakamura, Phys. Rev. D49 (1994), 4016[APS].
  6. M. Sasaki, Prog. Theor. Phys. 92 (1994), 17[PTP].
  7. H. Tagoshi and M. Sasaki, Prog. Theor. Phys. 92 (1994), 745[PTP].
  8. M. Shibata, M. Sasaki, H. Tagoshi and T. Tanaka, Phys. Rev. D51 (1995), 1646[APS].
  9. E. Poisson and M. Sasaki, Phys. Rev. D51 (1995), 5753[APS].
  10. S. Mano, H. Suzuki and E. Takasugi, Osaka University Preprint, OU-HET 237.
    S. Mano, Soryusiron Kenkyu (Kyoto) 92 (1995), C166.
  11. V. S. Otchik, Quantum Systems: New Trends and Methods (1995), p. 154.
  12. E. D. Fackerell and R. G. Crossman, J. Math. Phys. 9 (1977), 1849[AIP Scitation].
  13. A. Erdelyi et al., Higher Transcendental Equation, Vol. 1 (McGraw-Hill).
  14. S. A. Teukolsky and W. H. Press, Astrophys. J. 193 (1974), 443.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 96 No. 3 (1996) pp. 549-565 :
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  2. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 713-728 :
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  4. Progress of Theoretical Physics Vol. 97 No. 2 (1997) pp. 213-232 :
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  5. Progress of Theoretical Physics Vol. 98 No. 4 (1997) pp. 829-850 :
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  14. Progress of Theoretical Physics Vol. 112 No. 3 (2004) pp. 415-450 :
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  17. Progress of Theoretical Physics Vol. 113 No. 6 (2005) pp. 1165-1182 :
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  18. Progress of Theoretical Physics Vol. 115 No. 5 (2006) pp. 873-907 :
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  19. Progress of Theoretical Physics Vol. 117 No. 6 (2007) pp. 1041-1066 :
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  20. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 843-874 :
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  21. Progress of Theoretical Physics Vol. 127 No. 3 (2012) pp. 583-590 :
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  22. Progress of Theoretical Physics Vol. 128 No. 5 (2012) pp. 971-992 :
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  24. Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145 :
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