Invariant conserved currents in generalized gravity

TL;DR

This paper investigates conservation laws in generalized gravity theories, including non-Riemannian geometries and nonminimal couplings, deriving conserved currents and superpotentials applicable to extended microstructured bodies.

Contribution

It provides a unified framework for conservation laws in diverse gravity models, extending previous results to more general geometries and couplings.

Findings

Conserved currents are generated by arbitrary vector fields under certain conditions.

Explicit expressions for superpotentials are derived.

Conserved quantities relate to multipole moments of extended bodies.

Abstract

We study conservation laws for gravity theories invariant under general coordinate transformations. The class of models under consideration includes Einstein's general relativity theory as a special case as well as its generalizations to non-Riemannian spacetime geometry and nonminimal coupling. We demonstrate that an arbitrary vector field on the spacetime manifold generates a current density that is conserved under certain conditions, and find the expression of the corresponding superpotential. For a family of models including nonminimal coupling between geometry and matter, we discuss in detail the differential conservation laws and the conserved quantities defined in terms of covariant multipole moments. We show that the equations of motion for the multipole moments of extended microstructured test bodies lead to conserved quantities that are closely related to the conserved currents derived in the field-theoretic framework.