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Prog. Theor. Phys. Vol. 92 No. 1 (1994) pp. 17-36

[ Full Text PDF : FREE ACCESS (1613K) ]

Post-Newtonian Expansion of the Ingoing-Wave Regge-Wheeler Function

Misao Sasaki

Department of Physics, Kyoto University, Kyoto 606-01

(Received February 9, 1994)

Abstract:

We present a method of post-Newtonian expansion to solve the homogeneous Regge-Wheeler equation which describes gravitational waves on the Schwarzschild spacetime. The advantage of our method is that it allows a systematic iterative analysis of the solution. Then we obtain the Regge-Wheeler function which is purely ingoing at the horizon in closed analytic form, with accuracy required to determine the gravitational wave luminosity to (post)4-Newtonian order (i.e., order v8 beyond Newtonian) from a particle orbiting around a Schwarzschild black hole. Our result, valid in the small-mass limit of one body, gives an important guideline for the study of coalescing compact binaries. In particular, it provides basic formulas to analytically calculate detailed waveforms and luminosity, including the tail terms to (post)3-Newtonian order, which should be reproduced in any other post-Newtonian calculations.


URL : http://ptp.ipap.jp/link?PTP/92/17/
DOI : 10.1143/PTP.92.17

[ Full Text PDF : FREE ACCESS (1613K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 92 No. 4 (1994) pp. 745-771 :
    Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbit around a Schwarzschild Black Hole
    Hideyuki Tagoshi and Misao Sasaki
  2. Progress of Theoretical Physics Vol. 93 No. 2 (1995) pp. 307-333 :
    Post-Newtonian Expansion of Gravitational Waves from a Particle in Slightly Eccentric Orbit around a Rotating Black Hole
    Hideyuki Tagoshi
  3. Progress of Theoretical Physics Vol. 95 No. 6 (1996) pp. 1079-1096 :
    Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions
    Shuhei Mano, Hisao Suzuki and Eiichi Takasugi
  4. Progress of Theoretical Physics Vol. 96 No. 4 (1996) pp. 713-728 :
    Post-Newtonian Expansion of Gravitational Waves from a Compact Star Orbiting a Rotating Black Hole in Brans-Dicke Theory – Circular Orbit Case –
    Akira Ohashi, Hideyuki Tagoshi and Misao Sasaki
  5. Progress of Theoretical Physics Vol. 96 No. 6 (1996) pp. 1087-1101 :
    Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild Black Hole
    Takahiro Tanaka, Hideyuki Tagoshi and Misao Sasaki
  6. Progress of Theoretical Physics Vol. 98 No. 4 (1997) pp. 829-850 :
    Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole
    Hideyuki Tagoshi, Shuhei Mano and Eiichi Takasugi
  7. Progress of Theoretical Physics Vol. 99 No. 1 (1998) pp. 79-95 :
    Regularization of Gravitational Radiation Reaction Force
    Yasushi Mino
  8. Progress of Theoretical Physics Vol. 100 No. 3 (1998) pp. 507-521 :
    Regularization Method of Gravitational Radiation Reaction
    Yasushi Mino and Hiroyuki Nakano
  9. Progress of Theoretical Physics Vol. 106 No. 2 (2001) pp. 339-362 :
    Self-Force on a Scalar Charge in Circular Orbit around a Schwarzschild Black Hole
    Hiroyuki Nakano, Yasushi Mino and Misao Sasaki
  10. 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
  11. Progress of Theoretical Physics Supplement No.136 (1999) pp. 146-157 :
    Post-Newtonian Expansion of Gravitational Radiation
    Luc Blanchet
  12. Progress of Theoretical Physics Supplement No.136 (1999) pp. 158-167 :
    Generation of Post-Newtonian Gravitational Radiation via Direct Integration of the Relaxed Einstein Equations
    Clifford M. Will

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