A positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary

TL;DR

This paper proves a positive mass theorem for non-smooth, continuous metrics on asymptotically flat manifolds with non-compact boundary, extending classical results to less regular geometries.

Contribution

It establishes a positive mass theorem for metrics that are only continuous across a hypersurface, broadening the scope of geometric analysis in general relativity.

Findings

Positive mass theorem proven for non-smooth metrics

Extension to manifolds with non-compact corners

Applicable to metrics continuous across hypersurfaces

Abstract

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on manifolds with non-compact corners.