RADIATIVE EVOLUTION OF THE CARTER CONSTANT FOR GENERIC ORBITS AROUND A KERR BLACK-HOLE

Recently, we proposed a new approach for the radiative evolution of ge neric orbits around a Kerr black hole. This involves the calculation o f the evolution rate of all three constants of motion: The energy E, t he azimuthal angular momentum L(z), and the Carter constant Q. In a pr evious paper we presented the general approach, and outlined its appli cation to a scalar-field radiation reaction. In the present paper, we give the full details of the scalar-field calculations: We first deriv e the explicit expressions for E, L(z), and Q. Then, we compare our re sults for E and L(z) to those obtained from the standard method, and s how that they are in full agreement. In addition, we outline the appli cation of our method to the electromagnetic and gravitational radiatio n-reaction problem.