  We present unfolded description of AdS(4) black hole with generic parameters
of mass, NUT, magnetic and electric charges as well as two kinematical
parameters one of which is angular momentum. A flow with respect to black hole
parameters, that relates the obtained black hole unfolded system to the
covariant constancy condition for an AdS(4) global symmetry parameter, is
found. The proposed formulation gives rise to a coordinate-independent
description of the black hole metric in AdS(4). The black hole charges are
identified with flow evolution parameters while its kinematical constants are
the first integrals of the black hole unfolded system expressed via invariants
of the AdS(4) global symmetry parameter. It is shown how the proposed method
reproduces various known forms of black hole metrics including the Carter and
Kerr-Newman solutions. Free flow gauge parameters allow us to choose different
metric representations such as Kerr-Schild, double Kerr-Schild or generalized
Carter-Plebanski in the coordinate-independent way.
