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Prog. Theor. Phys. Vol. 115 No. 5 (2006) pp. 873-907

[ Full Text PDF : FREE ACCESS (332K) ]

Adiabatic Evolution of Orbital Parameters in Kerr Spacetime

Norichika Sago,1 Takahiro Tanaka,2 Wataru Hikida,3 Katsuhiko Ganz2 and Hiroyuki Nakano4

1Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan
2Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
3Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
4Department of Mathematics and Physics, Graduate School of Science, Osaka City University, Osaka 558-8585, Japan

(Received November 30, 2005)

Abstract:

We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.


URL : http://ptp.ipap.jp/link?PTP/115/873/
DOI : 10.1143/PTP.115.873

[ Full Text PDF : FREE ACCESS (332K) ] Citation:

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Citing Article(s) :

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  2. Progress of Theoretical Physics Vol. 118 No. 3 (2007) pp. 577-579 :
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    Hideyuki Tagoshi
  3. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 843-874 :
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    Ryuichi Fujita, Wataru Hikida and Hideyuki Tagoshi
  4. Progress of Theoretical Physics Vol. 127 No. 3 (2012) pp. 583-590 :
    Gravitational Radiation for Extreme Mass Ratio Inspirals to the 14th Post-Newtonian Order
    Ryuichi Fujita
  5. Progress of Theoretical Physics Vol. 128 No. 5 (2012) pp. 971-992 :
    Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order
    Ryuichi Fujita

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