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

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.