On Hypermomentum in General Relativity III. Coupling Hypermomentum to Geometry

Abstract

Abstract In Part I1 of this series we presented the notion of the material hypermomentum current and motivated its introduction into general relativity. In Part II2 we showed that a general, linearly connected manifold with symmetric metric (L4, g) is the appropriate geometrical framework for such an introduction. The present paper completes the picture by giving dynamical definitions for energy-momentum and hypermomentum for a minimally coupled material Lagrangian. We derive and discuss the field equations of a new metricaffine gravitational theory which embodies these notions.