Prog. Theor. Phys. Vol. 67 No. 6 (1982) pp. 1788-1809

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Gravitational Radiation from a Kerr Black Hole. I

— Formulation and a Method for Numerical Analysis —

Misao Sasaki and Takashi Nakamura

Research Institute for Fundamental Physics, Kyoto University, Kyoto 606

(Received November 28, 1981)

Abstract:

A class of new inhomogeneous equations governing gravitational perturbations of the Kerr geometry is presented. It is shown that, contrary to the case of the Teukolsky equation, the perturbation equations have short-range potential and no divergent source terms for large distance. Using one of such equations which seems to be the simplest, we have computed the spectrum and the energy of gravitational radiation induced by a test particle of mass µ falling along the z-axis into a Kerr black hole of mass M(≫µ) and angular momentum Ma(a<M). It is found that the total energy radiated is 0.0170µc² (µ/M) when a = 0.99M, which is 1.65 times larger than that when a = 0, i.e., the Schwarzschild case.

URL : http://ptp.ipap.jp/link?PTP/67/1788/
DOI : 10.1143/PTP.67.1788

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Citing Article(s) :

Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 815-827 :
On the Generation Mechanism of Gravitational Waves in the Vicinity of a Black Hole

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Progress of Theoretical Physics Vol. 70 No. 3 (1983) pp. 757-771 :
Energy, Momentum and Angular Momentum of Gravitational Waves Induced by a Particle Plunging into a Schwarzschild Black Hole

Ken-ichi Oohara and Takashi Nakamura
Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 79-90 :
Gravitational Radiation from a Particle with Orbital Angular Momentum Plunging into a Kerr Black Hole

Yasufumi Kojima and Takashi Nakamura
Progress of Theoretical Physics Vol. 72 No. 3 (1984) pp. 494-504 :
Gravitational Radiation from a Particle Scattered by a Kerr Black Hole

Yasufumi Kojima and Takashi Nakamura
Progress of Theoretical Physics Vol. 90 No. 3 (1993) pp. 595-614 :
Gravitational Waves Induced by a Particle Orbiting around a Rotating Black Hole

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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

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Progress of Theoretical Physics Vol. 105 No. 2 (2001) pp. 197-218 :
The Gravitational Reaction Force on a Particle in the Schwarzschild Background

Hiroyuki Nakano and Misao Sasaki
Progress of Theoretical Physics Vol. 112 No. 3 (2004) pp. 415-450 :
New Numerical Methods to Evaluate Homogeneous Solutions of the Teukolsky Equation

Ryuichi Fujita and Hideyuki Tagoshi
Progress of Theoretical Physics Supplement No.90 (1987) pp. 1-218 :
General Relativistic Collapse to Black Holes and Gravitational Waves from Black Holes

Takashi Nakamura, Kenichi Oohara and Yasufumi Kojima
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
Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145 :
Gravitational Radiation Reaction

Takahiro Tanaka