Unfolded description of AdS4 Kerr black hole

It is shown that AdS4 Kerr black hole is a solution of simple unfolded differential equations that form a deformation of the zero-curvature description of empty AdS4 space-time. Our construction uses the Killing symmetries of the Kerr solution. All known and some new algebraic properties of the Kerr-Schild solution result from the obtained black hole unfolded system in the coordinate-independent way. Kerr-Schild type solutions of free equations in AdS4 for massless fields of any spin associated with the proposed black hole unfolded system are found.