An f(R) gravitation for galactic environments

We propose an action- based f ( R) modification of Einstein's gravity that admits 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, calibrated empirically, is 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, [ arXiv: astroph/ 0610390]) that a) the gravitational waves in this spacetime propagate with the speed of light in vacuum and b) there is a lensing effect added to what one finds in the classic GR.