A spinorial quasilocal mass

TL;DR

This paper introduces a new spinorial method to define and analyze the quasilocal energy of a compact manifold with boundary, establishing positivity results in both Riemannian and Lorentzian geometries.

Contribution

It presents a novel spinorial construction for quasilocal energy that extends previous approaches and proves its positivity in multiple geometric settings.

Findings

Positivity of the quasilocal energy in Riemannian geometry

Positivity of the quasilocal energy in Lorentzian geometry

A new spinorial framework for quasilocal mass

Abstract

We define a quasilocal energy of a compact manifold-with-boundary, relative to a background manifold. The construction uses spinors on one manifold and the pullback of dual spinors from the other manifold. We prove positivity results for the quasilocal energy, in both the Riemannian and Lorentzian settings.