NEWTONIAN LIMIT OF CONFORMAL GRAVITY AND THE LACK OF NECESSITY OF THE2ND-ORDER POISSON EQUATION

We study the interior structure of a locally conformal invariant fourt h order theory of gravity in the presence of a static, spherically sym metric gravitational source. We find, quite remarkably, that the assoc iated dynamics is determined exactly and without any approximation at all by a simple fourth order Poisson equation which thus describes bot h the strong and weak field limits of the theory in this static case. We present the solutions to this fourth order equation and find that w e are able to recover all of the standard Newton-Euler gravitational p henomenology in the weak gravity limit, to thus establish the observat ional viability of the weak field limit of the fourth order theory. Ad ditionally, we make a critical analysis of the second order Poisson eq uation, and find that the currently available experimental evidence fo r its validity is not as clearcut and definitive as is commonly believ ed, with there not apparently being any conclusive observational suppo rt for it at all either on the very largest distance scales far outsid e of fundamental sources, or on the very smallest ones within their in teriors. Our study enables us to deduce that even though the familiar second order Poisson gravitational equation may be sufficient to yield Newton's Law of Gravity it is not in fact necessary.