Initial data set rigidity results for polyhedra

TL;DR

This paper establishes a dihedral rigidity result for polyhedral initial data sets using spinors, linking it to the positive mass theorem and trapped surfaces, and extends existing rigidity analysis methods.

Contribution

It introduces a novel spinor-based approach to dihedral rigidity in polyhedral initial data sets, connecting multiple geometric and physical concepts.

Findings

Proves dihedral rigidity for polyhedral initial data sets.

Connects rigidity results with the spacetime positive mass theorem.

Extends Beig-Chrusciel's rigidity analysis to twisted spinor bundles.

Abstract

Using spinors, we show a dihedral type rigidity for polyhedral initial data sets. This rigidity connects spacetime positive mass theorem, dihedral rigidity and capillary marginally trapped surfaces. Our method is to extend the rigidity analysis of spacetime positive mass theorem due to Beig-Chrusciel to the settings of a twisted spinor bundle.