  The classical action of quantum gravity, determined by renormalization,
contains infinitely many independent couplings and can be expressed in
different perturbatively equivalent ways. We organize it in a convenient form,
which is based on invariants constructed with the Weyl tensor. We show that the
FLRW metrics are exact solutions of the field equations in arbitrary
dimensions, and so are all locally conformally flat solutions of the Einstein
equations. Moreover, expanding the metric tensor around locally conformally
flat backgrounds the quadratic part of the action is free of higher
derivatives. Black-hole solutions of Schwarzschild and Kerr type are modified
in a non-trivial way. We work out the first corrections to their metrics and
study their properties.
