A Boundary-Local Mass Cocycle and the Mass of Asymptotically Hyperbolic Manifolds.

We construct a cocycle that, for a given -manifold, maps a pair of asymptotically locally hyperbolic (ALH) metrics to a tractor-valued -form field on the conformal infinity. This requires the metrics to be asymptotically related to a given order that depends on the dimension. It then provides a local geometric quantity on the boundary that is naturally associated to the pair and can be interpreted as a relative energy-momentum density.