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

Katsuhiko Ganz·Wataru Hikida·Hiroyuki Nakano·Norichika Sago·Takahiro Tanaka
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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.

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Katsuhiko Ganz, Wataru Hikida, Hiroyuki Nakano, Norichika Sago, Takahiro Tanaka. 2007-05-31. Adiabatic Evolution of three 'Constants' of Motion for Greatly Inclined Orbits in Kerr spacetime. https://doi.org/10.1143/ptp.117.1041

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