The Static Gravitational Field of a Spherically Symmetric Body

Abstract

We continue here the exam \cite{LuMa} of a theory of gravity that satisfies the Einstein Equivalence Principle (EEP) for any kind of matter/energy, except for the gravitational energy. This is part of a research program that intends to re-examine the standard Feynman-Deser approach of field theoretical derivation of Einstein\rq s General Relativity. The hypothesis implicit in such precedent derivations \cite{Feynman} \cite{Deser} concerns the universality of gravity interaction. Although there is a strong observational basis supporting the universality of matter to gravity interaction, there is not an equivalent situation that supports the hypothesis that gravity interacts with gravity as any other form of non-gravitational energy. We analyse here a kind of gravity-gravity interaction distinct from GR but, as we shall see, that conforms with the actual status of observation. We exhibit the gravitational field produced by a spherically symmetric static configuration as described in this field theory of gravity. The values that we obtain for the standard PPN parameters ($α= β= γ= 1$) coincide with those of General Relativity. Thus, as we pointed out in a previous paper, the main different aspect of our theory and GR concerns the velocity of the gravitational waves. Since there is a large expectation that the detection of gravitational waves will occur in the near future, the question of which theory describes Nature better will probably be settled soon.