The Positive Mass Theorem for Creased Initial Data

TL;DR

This paper proves a positive mass theorem for a new class of initial data with singularities, extending previous results and providing a rigidity statement under specific geometric conditions.

Contribution

It introduces a positive mass theorem for asymptotically flat spin initial data with codimension one singularities, generalizing prior work and including a rigidity aspect.

Findings

Establishes a positive mass theorem for singular initial data.

Provides a rigidity statement under matching Bartnik data conditions.

Extends previous results by Miao, Tsang, and Shi-Tam.

Abstract

We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bartnik data condition involving spacetime rotations, and discuss applications. This generalizes several previous works on the topic, including results of Miao, Tsang, and Shi-Tam.