Abstract
Conformal (Weyl) gravity has been advanced in the recent past as an alternative to General Relativity (GR). The theory has had some success in fitting galactic rotation curves without the need for copious amounts of dark matter. To check the viability of Weyl gravity, we calculate the deflection of light in the exterior of a static spherically symmetric source. The result for the deflection of light is remarkably simple: besides the usual positive (attractive) Einstein deflection of 4GM/r0 we obtain an extra deflection term of −γr0 where γ is a constant and r0 is the radius of closest approach. With a negative γ, the extra term can increase the deflection on large distance scales (galactic or greater) and therefore imitate the effect of dark matter. Notably, the negative sign required for γ is opposite to the sign of γ used to fit galactic rotation curves by Mannheim and Kazanas. We explain why the signs in the two analyses are different.
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