Intermediate behavior of Kerr tails

Abstract. The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed a puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole. In this paper we study late-time decay rates using a horizon-penetrating, hyperboloidal slicing with transmitting layers attached to a compact domain in Boyer–Lindquist coordinates. The technical construction of transmitting layers for Kerr spacetime should be useful in future studies of wave propagation. We discuss splitting of local decay rates in certain projected modes and in the full field. The splitting in the full field rates is explained by competition between projected modes. For the splitting in certain projected modes we argue that, asymptotically in time, the strong field rates are valid at all finite distances, but at any given late time, there are three domains with different local decay rates whose boundaries move during evolution. 1