Invariant conserved currents in generalized gravity
  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.
