OPEN QUESTIONS IN CLASSICAL GRAVITY

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second-order Newton-Einstein classical grav itational theory. On the observational side we discuss the degree to w hich the realm of validity of Newton's law of gravity can actually be extended to distances much larger than the solar system distance scale s on which the law was originally established. On the theoretical side we identify some commonly accepted (but actually still open to questi on) assumptions which go into the formulation of the standard second-o rder Einstein theory in the first place. In particular, we show that w hile the familiar second order Poisson gravitational equation (and acc ordingly its second-order covariant Einstein generalization) may be su fficient to yield Newton's law of gravity they are not in fact necessa ry. The standard theory thus still awaits the identification of some p rinciple which would then make it necessary too. We show that current observational information does not exclusively mandate the standard th eory, and that the conformal invariant fourth-order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the c onstraints of data, and in fact to do so without the need for any so f ar unobserved nonluminous or dark matter.