Solution of the Scalar Wave Equation in a Kerr Background by Separation of Variables

Abstract

The effect of the Kerr gravitational field on wave phenomena is explored by examining the inhomogeneous wave equation for a scalar massive field in a Kerr background geometry. The equation is separated in Boyer-Lindquist coordinates. The angular functions are spheroidal harmonics, and the radial equation is reduced to a one-dimensional Schr\"odinger equation with an effective potential.