Off-Shell ADT Conserved Quantities in Palatini Gravity

Abstract

In this paper we generalize the off-shell Abbott-Deser-Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein-Hilbert action, the most general $L(g_{\mu \nu },R^{\lambda }{}_{\nu \alpha \mu },T^{\lambda }{}_{\alpha \beta },Q_{\alpha \mu \nu })$ theories and the teleparallel Palatini gravity.

20 pages, version to be published in Class. Quantum Grav

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