Rotating discs on the Kerr black hole background

Analytical solution of a rotating black hole surrounded by accretion disc in full GR is, so far, unknown. The Ernst equation is nonlinear. In this talk, we will provide a framework in which the solutions of linearised Ernst equations can be obtained from the linear perturbations of Kerr black hole treated in the formalism of the Debye potentials. In this way, we recover all the metric perturbations in term of a single complex scalar function (which solves the Laplace equation).