  We study a black hole 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.
