Mass and Riemannian Polyhedra

2021/01/07 by Miao, Pengzi, Piubello, Annachiara
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2101.02693

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.

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