  A renormalization group (RG) improvement of the Einstein-Hilbert action is
performed which promotes Newton's constant and the cosmological constant to
scalar functions on spacetime. They arise from solutions of an exact RG
equation by means of a ``cutoff identification'' which associates RG scales to
the points of spacetime. The resulting modified Einstein equations for
spherically symmetric, static spacetimes are derived and analyzed in detail.
The modifications of the Newtonian limit due to the RG evolution are obtained
for the general case. As an application, the viability of a scenario is
investigated where strong quantum effects in the infrared cause Newton's
constant to grow at large (astrophysical) distances. For two specific RG
trajectories exact vacuum spacetimes modifying the Schwarzschild metric are
obtained by means of a solution-generating Weyl transformation. Their possible
relevance to the problem of the observed approximately flat galaxy rotation
curves is discussed. It is found that a power law running of Newton's constant
with a small exponent of the order $10^{-6}$ would account for their
non-Keplerian behavior without having to postulate the presence of any dark
matter in the galactic halo.
