The positive mass Theorem and Penrose inequality for graphical manifolds

TL;DR

This paper provides elementary formulas for the ADM mass of graphical manifolds, enabling proofs of the positive mass theorem and Penrose inequality for this class, including those with flat normal bundles.

Contribution

It introduces explicit formulas for ADM mass that simplify proofs of fundamental geometric inequalities for graphical manifolds.

Findings

Positive mass theorem proven for a class of graphical manifolds

Penrose inequality established using elementary methods

Includes manifolds with flat normal bundle as special cases

Abstract

We give, via elementary methods, explicit formulas for the ADM mass which allow us to conclude the positive mass theorem and Penrose inequality for a class of graphical manifolds which includes, for instance, that ones with flat normal bundle.