Dynamical renormalization of black-hole spacetimes

We construct a black-hole spacetime which includes the running of the gravitational coupling in a selfconsistent way. Starting from a classical Schwarzschild black hole, the backreaction effects produced by the running Newton's coupling are taken into account iteratively. The sequence, described by a simple recurrence relation, flows towards a self-consistent solution that can be derived analytically. As a key result, if the gravitational renormalization group flow attains a non-trivial fixed point at high energies, the sequence converges to a renormalized black-hole spacetime of the Dymnikova-type, which is free of singularities.