Open Questions in Classical Gravity

TL;DR

This paper examines open questions about the validity and uniqueness of classical gravity theories, questioning assumptions of Einstein's framework and exploring alternative models that fit observational data without dark matter.

Contribution

It challenges the necessity of second order Einstein gravity and presents conformal invariant fourth order gravity as a viable alternative consistent with observations.

Findings

Standard Einstein gravity is not uniquely mandated by data.

Fourth order conformal gravity can explain observations without dark matter.

Some assumptions in deriving Einstein's equations are still open to question.

Abstract

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's Law of Gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted but actually still open to question assumptions which go into the formulating of the standard second order Einstein theory in the first place. In particular, we show that while the familiar second order Poisson gravitational equation (and accordingly its second order covariant Einstein generalization) may be sufficient to yield Newton's Law of Gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved non-luminous or dark matter.