A ug 1 99 7 Classical tests for Weyl gravity : deflection of light and radar echo delay

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 propose two additional classical tests of the theory: the deflection of light and the radar echo delay 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/r 0 we obtain an extra deflection term of −γr 0 where γ is a constant and r 0 is the radius of closest approach. By a suitable choice of γ the extra term can be made significant on large distance scales (galactic or greater) where dark matter effects have been observed. The extra term must be positive (attractive) if it is to replace or imitate the effects of the presumed dark matter and therefore the sign of γ must be negative. Notably, this is the opposite sign of the γ used to fit galactic rotation curves. This throws a shadow on the explanation of flat rotation curves afforded by Weyl gravity.