Black hole solution for scale-dependent gravitational couplings and the corresponding coupling flow

We study a particular solution for the generalized Einstein Hilbert action with scale-dependent couplings G(r) and Lambda (r). The form of the couplings is not imposed, but rather deduced from the existence of a non-trivial symmetrical solution. A classical-like choice of the integration constants is found. Finally, the induced flow of the couplings is derived and compared to the flow that is obtained in the context of the exact renormalization group approach.