Conserved quantities for asymptotically AdS spacetimes in quadratic curvature gravity in terms of a rank-4 tensor

We investigate the conserved quantities associated to Killing isometries for asymptotically AdS spacetimes within the framework of quadratic-curvature gravity. By constructing a rank-4 tensor possessing the same index symmetries as the ones of the Riemann tensor, we propose a 2-form potential resembling the Noether one for quadratic-curvature gravity. Such a potential is compared with the results via other methods existing in the literature to establish the equivalence. Then this potential is adopted to define conserved quantities of asymptotically AdS spacetimes. As applications, we explicitly compute the mass of static spherically symmetric spacetimes, as well as the mass and the angular momentum for rotating spacetimes, such as the four(higher)-dimensional Kerr-AdS black holes and black strings embedded in quadraticcurvature gravities. Particularly, we emphasize the conserved charges of Einstein-Gauss-Bonnet, Weyl, and critical gravities, together with the ones for the asymptotically AdS solutions satisfying vacuum Einstein field equations.