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

TL;DR

This paper introduces a new tensor for Lovelock gravity in AdS spacetimes to define conserved charges and generalizes the approach to arbitrary diffeomorphism invariant gravity theories using a Komar-like formula.

Contribution

It proposes a novel rank-four tensor for conserved charges in Lovelock gravity and extends the concept to general gravity theories with a new Komar-like formula.

Findings

New divergenceless tensor for Lovelock gravity

Generalized tensor for arbitrary diffeomorphism invariant theories

Proposed a Komar-like formula for conserved charges

Abstract

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) spacetimes. 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.