High-order tail in 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 up 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 $t^{-2\ell-3}$, and at third order we obtain a logarithmic correction, $t^{-2\ell-5}\ln t$, where $\ell$ is the field multipole.