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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 $L(g_{mu u}, R^{lambda}{}_{ ualphamu}, T^{lambda}{}_{alphabeta}, Q_{alphamu u})$ theories and the teleparallel Palatini gravity.
Using the {it off-shell} Noether current and potential we compute the entropy for the AdS black holes in new massive gravity. For the non-extremal BTZ black holes by implementing the so-called stretched horizon approach we reproduce the correct expre
A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and conformal
We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fl
We study non-Einstein Bach-flat gravitational instanton solutions that can be regarded as the generalization of the Taub-NUT/Bolt and Eguchi-Hanson solutions of Einstein gravity to conformal gravity. These solutions include non-Einstein spaces which
We construct conserved quantities in pure Lovelock gravity for both static and dynamic Vaydia-type black holes with AdS, dS and flat asymptotics, applying field-theoretical formalism developed earlier. Global energy (where applicable), quasi-local en