Exact black hole solution for scale dependent gravitational couplings and the corresponding coupling flow

Understand

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.