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Within the framework of the Lovelock gravity theory, we propose a newrank-four divergenceless tensor consisting of the Riemann curvature tensor andinheriting its algebraic symmetry characters. Such a tensor can be adopted todefine conserved charges of the Lovelock gravity theory in asymptoticallyanti-de Sitter (AdS) spacetimes. Besides, inspired with the case of theLovelock gravity, we put forward another general fourth-rank tensor in thecontext of an arbitrary diffeomorphism invariant theory of gravity described bythe Lagrangian constructed out of the curvature tensor. On basis of thenewly-constructed tensor, we further suggest a Komar-like formula for theconserved charges of this generic gravity theory.

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