Conformal gravity does not predict flat galaxy rotation curves

Understand

We reconsider the widely held view that the Mannheim--Kazanas (MK) vacuum solution for a static, spherically-symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those observed in galaxies, without the need for dark matter.

• This prediction assumes that test particles have fixed rest mass and follow timelike geodesics in the MK metric in the vacuum region exterior to a spherically-symmetric representation of the galactic mass distribution.
• Such geodesics are not conformally invariant, however, which leads to an apparent discrepancy with the analogous calculation performed in the conformally-equivalent Schwarzschild-de-Sitter (SdS) metric, where the latter does not predict flat rotation curves.
• This difference arises since the mass of particles in CG must instead be generated dynamically through interaction with a scalar field.