Adiabatic Evolution of Orbital Parameters in Kerr Spacetime

We investigate the adiabatic orbital evolution of a point particle in theKerr spacetime due to the emission of gravitational waves. In the case that thetimescale of the orbital evolution is enough smaller than the typical timescaleof orbits, the evolution of orbits is characterized by the change rates ofthree constants of motion, the energy $E$, the azimuthal angular momentum $L$,and the Carter constant $Q$. For $E$ and $L$, we can evaluate their changerates from the fluxes of the energy and the angular momentum at infinity and onthe event horizon according to the balance argument. On the other hand, for theCarter constant, we cannot use the balance argument because we do not know theconserved current associated with it. %and the corresponding conservation law.Recently, Mino proposed a new method of evaluating the averaged change rate ofthe Carter constant by using the radiative field. In our previous paper wedeveloped a simplified scheme for practical evaluation of the evolution of theCarter constant based on the Mino's proposal. In this paper we describe ourscheme in more detail, and derive explicit analytic formulae for the changerates of the energy, the angular momentum and the Carter constant.Comment: 34 pages, no figur