II - Conservation of Gravitational Energy Momentum and Poincare-Covariant Classical Theory of Gravitation

TL;DR

This paper develops a Poincaré-covariant classical theory of gravitation by formulating a gauge theory of volume-preserving diffeomorphisms, deriving field equations, and demonstrating recovery of Newton's law and gravitational radiation.

Contribution

It introduces a novel gauge-theoretic approach to gravity based on volume-preserving diffeomorphisms and derives Poincaré-covariant field equations with solutions.

Findings

Recovery of Newton's inverse square law in the static limit

Validation of the Weak Equivalence Principle in the approximation

Calculation of gravitational radiation from accelerated particles

Abstract

Viewing gravitational energy-momentum $p_G^\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\mu$ naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space ${\bf M}^{\sl 4}$. To extract its physical content the full gauge group is reduced to its Poincar\'e subgroup. The respective Poincar\'e gauge fields, field strengths and Poincar\'e-covariant field equations are obtained and point-particle source currents are derived. The resulting set of non-linear field equations coupled to point matter is solved in first order resulting in Lienard-Wiechert-like potentials for the Poincar\'e fields. After numerical identification of gravitational and inertial energy-momentum Newton's inverse square law for gravity in the static non-relativistic limit is recovered. The Weak Equivalence Principle in this approximation is proven to be valid and spacetime geometry in the presence of Poincar\'e fields is shown to be curved. Finally, the gravitational radiation of an accelerated point particle is calulated.