Radiative evolution of the Carter constant for generic orbits around a Kerr black hole

Abstract

Recently, we proposed a new approach for the radiative evolution of generic orbits around a Kerr black hole. This involves the calculation of the evolution rate of all three constants of motion: The energy E, the azimuthal angular momentum ${L}_{z}$, and the Carter constant Q. In a previous paper we presented the general approach, and outlined its application to a scalar-field radiation reaction. In the present paper, we give the full details of the scalar-field calculations: We first derive the explicit expressions for \ifmmode \dot{E}\else \.{E}\fi{}, ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{L}}_{z}$, and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{Q}$. Then, we compare our results for \ifmmode \dot{E}\else \.{E}\fi{} and ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{L}}_{z}$ to those obtained from the standard method, and show that they are in full agreement. In addition, we outline the application of our method to the electromagnetic and gravitational radiation-reaction problem.