  We propose an action-based $ f(R) $ modification of Einstein's gravity which
admits of a modified Schwarzschild-deSitter metric. In the weak field limit
this amounts to adding a small logarithmic correction to the newtonian
potential. A test star moving in such a spacetime acquires a constant
asymptotic speed at large distances. This speed turns out to be proportional to
the fourth root of the mass of the central body in compliance with the
Tully-Fisher relation. A variance of MOND's gravity emerges as an inevitable
consequence of the proposed formalism. It has also been shown (Mendoza et al.
2006) that a) the gravitational waves in this spacetime propagate with the
speed of light in vacuum and b) there is a lensing effect additional to what
one finds in the classic GR.
