MG11 
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Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in covariant and noncovariant(ly looking) ways. A mathematical fact underlies such a diversity: there is an ambiguity in the definition of the covariant generalization of the Lie derivative. We develop a general approach to construction of invariant conserved currents generated by an arbitrary vector field. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. As an outcome, we present a derivation of the Komar construction for the total mass and angular momentum of compact field configurations. A development of the ``regularization via relocalization" scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate our formalism by some explicit examples.