A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization.

Within the framework of the Lovelock gravity theory, we propose a new rank-4 divergenceless tensor consisting of the Riemann curvature tensor and inheriting its symmetries. Such a tensor can be applied to define conserved charges of the Lovelock gravity theory in asymptotically AdS spacetimes. Besides, inspired with the case of the Lovelock gravity, we put forward another two general forth-rank tensors in the context of an arbitrary gravity theory described by the Lagrangian constructed out of the curvature tensor. On basis of each of the two newly-constructed tensors, we further suggest a Komar-like formula for the conserved charges of this gravity theory.