Interpreting Mass via Riemannian Polyhedra

TL;DR

This paper explores the relationship between mass in general relativity and the geometry of Riemannian polyhedra in different asymptotic settings, providing new geometric insights into gravitational mass.

Contribution

It introduces a novel connection between gravitational mass and Riemannian polyhedral geometry in asymptotically flat and hyperbolic manifolds.

Findings

Establishes a geometric interpretation of mass via Riemannian polyhedra

Extends the concept of mass to asymptotically hyperbolic manifolds

Provides a framework linking geometric structures to gravitational properties

Abstract

We give an account of some recent development that connects the concept of mass in general relativity to the geometry of large Riemannian polyhedra, in the setting of both asymptotically flat and asymptotically hyperbolic manifolds.