Density and positive mass theorems for initial data sets with boundary

TL;DR

This paper establishes a density theorem for asymptotically flat initial data with boundary under the dominant energy condition, and proves the spacetime positive mass theorem with rigidity for such data in dimensions less than 8 without requiring a spin condition.

Contribution

It introduces a harmonic asymptotics density theorem and proves the positive mass theorem with rigidity for initial data sets with boundary, removing the spin assumption in certain dimensions.

Findings

Proves a density theorem for initial data with boundary.

Establishes the positive mass theorem with rigidity in dimensions less than 8.

Removes the spin assumption requirement in the positive mass theorem.

Abstract

We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for initial data sets with apparent horizon boundary in dimensions less than $8$ without a spin assumption.