CLASSICAL TESTS FOR WEYL GRAVITY - DEFLECTION OF LIGHT AND TIME-DELAY- ART. NO. 024011

Weyl gravity has been advanced in the recent past as an alternative to general relativity. The theory has had some success in fitting galact ic rotation curves without the need for copious amounts of dark matter . To check the viability of Weyl gravity, we propose two additional cl assical tests of the theory: the deflection of light and time delay in the exterior of a static spherically symmetric source. The result for the deflection of light is remarkably simple: in addition to the usua l positive (attractive) Einstein deflection of 4GM/r(o), we obtain an extra deflection term of - gamma r(0) where gamma is a constant and r( 0) is the radius of closest approach. With a negative gamma, the extra term can increase the deflection on large distance scales (galactic o r greater) and therefore imitate the effect of dark matter. Notably, t he negative sign required for gamma is opposite to the sign of gamma u sed to fit galactic rotation curves. The experimental constraints show explicitly that the magnitude of gamma is of the order of the inverse Hubble length something already noted as an interesting numerical coi ncidence in the fitting of galactic rotation curves. [S0556-2821(98)05 514-3].