Within the framework of the Lovelock gravity theory, we propose a new rank-four divergenceless tensor consisting of the Riemann curvature tensor and inheriting its algebraic symmetry characters. Such a tensor can be adopted to define conserved charges of the Lovelock gravity theory in asymptotically anti-de Sitter (AdS) space–times. Besides, inspired with the case of the Lovelock gravity, we put forward another general fourth-rank tensor in the context of an arbitrary diffeomorphism invariant theory of gravity described by the Lagrangian constructed out of the curvature tensor. On basis of the newly-constructed tensor, we further suggest a Komar-like formula for the conserved charges of this generic gravity theory.

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AdS时空洛夫洛克引力守恒电荷的新公式及其推广

在洛夫洛克引力理论的框架内，我们提出了一个新的四阶无散张量，由黎曼曲率张量组成，并继承了其代数对称性。可以采用这样的张量来定义洛夫洛克引力理论在渐近反德西特 (AdS) 时空中的守恒电荷。此外，受洛夫洛克引力案例的启发，我们在由曲率张量构成的拉格朗日描述的任意微分同胚不变量引力理论的背景下，提出了另一个通用的四阶张量。在新构建的张量的基础上，我们进一步提出了一个类 Komar 公式来表示这个通用引力理论的守恒电荷。