  We provide a fully-covariant expression for the diffeomorphic charge in 4D
anti-de Sitter gravity, when the Gauss-Bonnet and Pontryagin terms are added to
the action. The couplings of these topological invariants are such that the
Weyl tensor and its dual appear in the on-shell variation of the action, and
such that the action is stationary for asymptotic (anti) self-dual solutions in
the Weyl tensor. In analogy with Euclidean electromagnetism, whenever the
self-duality condition is global, both the action and the total charge are
identically vanishing. Therefore, for such configurations the magnetic mass
equals the Ashtekhar-Magnon-Das definition.
