On the positivity of a quasi-local mass in general dimensions

TL;DR

This paper extends the positivity of a quasi-local mass integral to higher dimensions using spinor methods, building on previous results in three dimensions and employing monotonicity in quasi-spherical foliations.

Contribution

It generalizes the positivity result of Shi and Tam's quasi-local mass to higher dimensions with a new proof based on spinor techniques.

Findings

Positivity of quasi-local mass in higher dimensions established

Monotonicity of mass integral in quasi-spherical foliation demonstrated

Extension of Wang and Yau's positive mass theorem to higher dimensions

Abstract

In this paper, we obtain a positivity result of a quasi-local mass integral as proposed by Shi and Tam in general dimensions. The main argument is based on the monotonicity of a mass integral in a foliation of quasi-spherical metrics and a positive mass type theorem which was proved by Wang and Yau in the three dimensional case, and is shown here in higher dimensions using spinor methods.