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 theories and the teleparallel Palatini gravity.

中文翻译：

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壳外ADT守恒的帕拉蒂尼量

在本文中，我们将带壳的Abbott-Deser-Tekin（ADT）保守电荷形式主义推广到具有扭转和非度量性的Palatini重力理论。我们的构建基于坐标形式主义，独立的动态字段是度量和仿射连接。对于一般的帕拉蒂尼引力理论，它是一个直至边界项的不定形不变性，我们获得了离壳ADT势的最通用表达。作为明确的例子，我们得出了爱因斯坦-希尔伯特动作的壳外ADT势，最一般的理论和远距平行的帕拉蒂尼引力。