The Static Gravitational Field of a Spherically Symmetric Body

TL;DR

This paper explores a gravity theory satisfying the Einstein Equivalence Principle for matter but not for gravitational energy, deriving a static spherically symmetric gravitational field with PPN parameters matching GR, but differing in gravitational wave velocity.

Contribution

It presents a field theory of gravity that aligns with observations for matter interactions and reproduces GR's PPN parameters, while proposing a different gravitational wave velocity.

Findings

PPN parameters match those of GR: α=β=γ=1

Gravitational field of a static sphere derived in this theory

Main difference from GR is in gravitational wave velocity

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 ($\alpha = \beta = \gamma = 1$) 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.