We give a detailed review of construction of conserved quantities in extended theories of gravity for asymptotically maximally symmetric spacetimes and carry out explicit computations for various solutions. Our construction is based on the Killing charge method, and a proper discussion of the conserved charges of extended gravity theories with this method requires studying the corresponding charges in Einstein's theory with or without a cosmological constant. Hence we study the ADM charges (in the asymptotically flat case but in generic viable coordinates), the AD charges (in generic Einstein spaces, including the anti-de Sitter spacetimes) and the ADT charges in anti-de Sitter spacetimes. We also discuss the conformal properties and the behavior of these charges under large gauge transformations as well as the linearization instability issue which explains the vanishing charge problem for some particular extended theories. We devote a long discussion to the quasi-local and off-shell generalization of conserved charges in the 2+1 dimensional Chern-Simons like theories and suggest their possible relevance to the entropy of black holes.

中文翻译：

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扩展引力理论中的守恒电荷

我们详细回顾了渐近最大对称时空的扩展引力理论中守恒量的构造，并对各种解进行了显式计算。我们的构建基于杀伤电荷法，用这种方法适当讨论扩展引力理论的守恒电荷需要研究爱因斯坦理论中的相应电荷，无论是否有宇宙学常数。因此，我们研究了 ADM 电荷（在渐近平坦的情况下但在通用可行坐标中）、AD 电荷（在通用爱因斯坦空间中，包括反德西特时空）和反德西特时空中的 ADT 电荷。我们还讨论了这些电荷在大规范变换下的共形特性和行为以及线性化不稳定性问题，这解释了某些特定扩展理论的电荷消失问题。我们对 2+1 维陈-西蒙理论中守恒电荷的准局部和壳外推广进行了长时间的讨论，并提出了它们与黑洞熵的可能相关性。