Off-Shell ADT Conserved Quantities in Palatini Gravity

TL;DR

This paper extends the off-shell ADT conserved charge formalism to Palatini gravity theories, including torsion and non-metricity, providing a general framework for calculating conserved quantities in these extended gravitational models.

Contribution

It introduces a generalized off-shell ADT formalism for Palatini gravity with torsion and non-metricity, applicable to various gravity theories including teleparallel Palatini gravity.

Findings

Derived the off-shell ADT potential for Einstein-Hilbert action.

Formulated the general off-shell ADT potential for complex Palatini theories.

Applied the formalism to teleparallel 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.