Problems with Mannheim's conformal gravity program

TL;DR

The paper critiques Mannheim's conformal gravity, showing it fails to replicate Newtonian gravity at short distances without singularities and conflicts with laboratory experiments and galaxy rotation data.

Contribution

It provides a critical analysis demonstrating that Mannheim's conformal gravity cannot reconcile with experimental tests and galaxy observations without problematic assumptions.

Findings

Fails to reduce to Newtonian gravity without singularities

Conflicts with Cavendish-type experiments on Earth

Produces negative linear potential for positive proton mass

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.