# Positive mass theorem for initial data sets with corners along a hypersurface

## TL;DR

This paper establishes a positive mass theorem for certain initial data sets in Einstein-Maxwell and supergravity theories, even with non-smooth metrics and across hypersurfaces with corners, extending previous results to less regular and more general geometries.

## Contribution

It proves a positive mass theorem for initial data with corners along a hypersurface, removing assumptions of completeness and simple connectivity, in both 4D and 5D gravitational theories.

## Key findings

- Positive mass theorem holds for non-smooth initial data with corners.
- Results apply to manifolds with boundary and non-positive mean curvature.
- Extends previous theorems to less regular and more general initial data.

## Abstract

We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein) asymptotically flat or asymptotically cylindrical, for 4-dimensional Einstein-Maxwell theory and $5$-dimensional minimal supergravity theory which metrics fail to be $C^1$ and second fundamental forms and electromagnetic fields fail to be $C^0$ across an axially symmetric hypersurface $\Sigma$. Furthermore, we remove the completeness and simple connectivity assumptions in this result and prove it for manifold with boundary such that the mean curvature of the boundary is non-positive.