Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime

Details Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime

2007-02-09

arxiv.org/abs/gr-qc/0702054v2

Prog.Theor.Phys.117:1041-1066,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26pages, to be published in Progress of Theoretical Physics

Scientific paper

10.1143/PTP.117.1041

General orbits of a particle of small mass $\mu$ 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.

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