Scalar-Tensor Gravitational Strain Field Equations and the Longitudinal Wave Form

Abstract

From modern observations of gravitational interactions, it can be inferred that there is much left to discover about the fundamental gravitational field. Since the advent of the General Theory of Relativity over a century ago, we have come to make exotic assumptions pertaining to the inner workings of an associated field theory. One of which is an elastic nature to spacetime and the behavior of gravity for strong and weak fields. In this work we investigate a more \textit{physical} nature, expanding upon general relativity led by observations of strong sources. We introduce a candidate Lorentz-invariant field theory that employs an \textit{elastic} and \textit{pseudoscalar} nature to the field interpretation and it's properties. A unique generation of the Euler-Lagrange equations of motion is presented; resulting in a longitudinal wave equation for the \textit{Dilation} gravitational field. This provides a modern advancement of a relativistic gravitational field theory, supported by observation.