High-order late-time tail in a Kerr spacetime

We investigate the late-time tail of the retarded Green function for the dynamics of a linear field perturbation of Kerr spacetime. We develop an analytical formalism for obtaining the late-time tail to arbitrary order for general integer spin of the field. We then apply this formalism to obtain the details of the first five orders in the late-time tail of the Green function for the case of a scalar field. To leading order we recover the known power-law tail t(-2l-3), and at third order we obtain a new logarithmic correction, t(-2l-5) ln t, where l is the field multipole.