Problems with Mannheim’s conformal gravity program

Abstract

We show that Mannheim's conformal gravity program, whose potential has a term proportional to $1/r$ and another term proportional to $r$, does not reduce to Newtonian gravity at short distances, unless one assumes undesirable singularities of the mass density of the proton. Therefore, despite the claim that it successfully explains galaxy rotation curves, unless one assumes the singularities, it seems to be falsified by numerous Cavendish-type experiments performed at laboratories on Earth whose work have not found any deviations from Newton's theory. Moreover, it can be shown that as long as the total mass of the proton is positive, Mannheim's conformal gravity program leads to negative linear potential, which is problematic from the point of view of fitting galaxy rotation curves, which necessarily requires positive linear potential.