### 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.

Original language | English |
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Pages (from-to) | 1041-1066 |

Number of pages | 26 |

Journal | Progress of Theoretical Physics |

Volume | 117 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*117*(6), 1041-1066. https://doi.org/10.1143/PTP.117.1041

**Adiabatic evolution of three 'constants' of motion for greatly inclined orbits in kerr spacetime.** / Ganz, Katsuhiko; Hikida, Wataru; Nakano, Hiroyuki; Sago, Norichika; Tanaka, Takahiro.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 117, no. 6, pp. 1041-1066. https://doi.org/10.1143/PTP.117.1041

}

TY - JOUR

T1 - Adiabatic evolution of three 'constants' of motion for greatly inclined orbits in kerr spacetime

AU - Ganz, Katsuhiko

AU - Hikida, Wataru

AU - Nakano, Hiroyuki

AU - Sago, Norichika

AU - Tanaka, Takahiro

PY - 2007/6/1

Y1 - 2007/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34548613643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548613643&partnerID=8YFLogxK

U2 - 10.1143/PTP.117.1041

DO - 10.1143/PTP.117.1041

M3 - Article

AN - SCOPUS:34548613643

VL - 117

SP - 1041

EP - 1066

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 6

ER -