A boundary-local mass cocycle and the mass of asymptotically hyperbolic manifolds (Q6629001)

The aim of this paper is to construct new invariants that capture a notion of mass density, in the setting of asymptotically hyperbolic metrics. These invariants are locally defined (as quantities on the boundary at infinity) as volume forms with values in the standard tractor bundle associated to a conformal structure on the boundary, which has rank \(n + 1\) and carries a natural Lorentzian bundle metric. In the special case of hyperbolic space as a background, it is proved that these local quantities can be integrated to global parallel sections of the tractor bundle and then naturally recover the mass as introduced by \textit{X. Wang} [J. Differ. Geom. 57, No. 2, 273--299 (2001; Zbl 1037.53017)] and \textit{P. T. Chruściel} and \textit{M. Herzlich} [Pac. J. Math. 212, No. 2, 231--264 (2004; Zbl 1056.53025)].