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We study numerically the late-time tails of linearized fields with any spin$s$ in the background of a spinning black hole. Our code is based on theingoing Kerr coordinates, which allow us to penetrate through the eventhorizon. The late time tails are dominated by the mode with the least multipolemoment $\ell$ which is consistent with the equatorial symmetry of the initialdata and is equal to or greater than the least radiative mode with $s$ and theazimuthal number $m$.Comment: 5 pages, 4 Encapsulated PostScript figures; Accepted to Phys. Rev. D  (Rapid Communication

Radiative falloff in the background of rotating black holes