2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/205179It is shown that $AdS_4$ Kerr black hole is a solution of simple unfolded differential equations that form a deformation of the zero-curvature description of empty $AdS_4$ 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 $AdS_4$ for massless fields of any spin, associated to the proposed black hole unfolded system, are found.18 pagesGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext