How fast can a black hole eat?

We construct stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation. We discuss the relevance of these solutions for a decision on the following question: Does the limitation of the luminosity (Eddington limit) also imply an upper bound to the possible rate of mass flow? The question remains open until all instabilities have been studied. At the moment we still tend to a negative answer.