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Prog. Theor. Phys. Vol. 117 No. 6 (2007) pp. 1041-1066

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Adiabatic Evolution of Three `Constants' of Motion for Greatly Inclined Orbits in Kerr Spacetime

Katsuhiko Ganz,1 Wataru Hikida,2 Hiroyuki Nakano,3 Norichika Sago4 and Takahiro Tanaka1

1Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
2Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
3Department of Physics and Astronomy, and Center for Gravitational Wave Astronomy, The University of Texas at Brownsville, Brownsville, Texas 78520, USA
4School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

(Received February 14, 2007)

Abstract:

General orbits of a particle of small mass µ around a Kerr black hole of mass M are characterized by three parameters: the energy, the angular momentum and the Carter constant. The time-averaged rates of change of the energy and the angular momentum can be obtained by computing the corresponding fluxes of gravitational waves emitted by the particle. By contrast, the time-averaged rate of change of the Carter constant cannot be expressed as a flux of gravitational waves. Recently a method to compute this rate of change was proposed by Mino, and we refined it into a simplified form. In this paper we further extend our previous work to give a new formulation without the aid of expansion in terms of a small inclination angle.


URL : http://ptp.ipap.jp/link?PTP/117/1041/
DOI : 10.1143/PTP.117.1041

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 118 No. 3 (2007) pp. 577-579 :
    Post-Newtonian Expansion of Gravitational Waves from a Particle in Slightly Eccentric Orbit around a Rotating Black Hole
    Hideyuki Tagoshi
  2. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 843-874 :
    An Efficient Numerical Method for Computing Gravitational Waves Induced by a Particle Moving on Eccentric Inclined Orbits around a Kerr Black Hole
    Ryuichi Fujita, Wataru Hikida and Hideyuki Tagoshi

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