Mass and Riemannian Polyhedra

Abstract

We show that the concept of the ADM mass in general relativity can be understood as the limit of the total mean curvature plus the total defect of dihedral angle of the boundary of large Riemannian polyhedra. We also express the $n$-dimensional mass as a suitable integral of geometric quantities that determine the $(n-1)$-dimensional mass.

17 pages, 4 figures

Cited by in corpus (2)

• Dihedral rigidity for cubic initial data sets
• Mass and polyhedra in asymptotically hyperbolic manifolds