  Quantum corrections to the classical field equations, induced by a scale
dependent gravitational constant, are analyzed in the case of the static
isotropic metric. The requirement of general covariance for the resulting
non-local effective field equations puts severe restrictions on the nature of
the solutions that can be obtained. In general the existence of vacuum
solutions to the effective field equations restricts the value of the
gravitational scaling exponent $\nu^{-1}$ to be a positive integer greater than
one. We give further arguments suggesting that in fact only for $\nu^{-1}=3$
consistent solutions seem to exist in four dimensions.
