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

Katsuhiko Ganz, Wataru Hikida, Hiroyuki Nakano, Norichika Sago, Takahiro Tanaka

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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 languageEnglish
Pages (from-to)1041-1066
Number of pages26
JournalProgress of Theoretical Physics
Issue number6
Publication statusPublished - Jun 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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