  Using effective field theory techniques, we compute quantum corrections to
spherically symmetric solutions of Einstein's gravity and focus in particular
on the Schwarzschild black hole. Quantum modifications are covariantly encoded
in a non-local effective action. We work to quadratic order in curvatures
simultaneously taking local and non-local corrections into account. Looking for
solutions perturbatively close to that of classical general relativity, we find
that an eternal Schwarzschild black hole remains a solution and receives no
quantum corrections up to this order in the curvature expansion. In contrast,
the field of a massive star receives corrections which are fully determined by
the effective field theory.
