In this paper we elevate the formalism for off-shell Abbott-Deser-Tekin (ADT) conserved charges in the presence of arbitrary matter fields to including the internal gauge transformation, when the gauge fields are present. For this purpose, we resort to exact symmetry, and the symmetry generator is combined by diffeomorphism and internal gauge transformation. For universality, we consider an apparently non-covariant Lagrangian, which contains a matter Chern-Simons term. We show that the elevated off-shell ADT formalism is equivalent to the covariant phase space method and the Barnich-Brandt-Comp\`ere (BBC) formalism. To check the validity of our method, we explicitly compute the conserved charges of general non-extremal rotating charged G\"odel black holes in minimal five-dimensional gauged supergravity, reproducing the previously known results.

中文翻译：

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存在物质Chern-Simons项的广义壳外ADT守恒电荷

在本文中，我们将在任意物质场存在的情况下壳外 Abbott-Deser-Tekin (ADT) 守恒电荷的形式化提升为包括内部规范变换，当规范场存在时。为此，我们求助于精确对称，对称生成器通过微分同胚和内部规范变换相结合。为了普遍性，我们考虑一个明显非协变的拉格朗日，它包含一个物质陈-西蒙斯项。我们表明，提升的壳外 ADT 形式主义等效于协变相空间方法和 Barnich-Brandt-Comp\`ere (BBC) 形式主义。为了检查我们方法的有效性，我们明确地计算了一般非极值旋转带电 G\" 模型黑洞在最小五维超引力中的守恒电荷，