Density and positive mass theorems for initial data sets with boundary

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.

arXiv comment33 pages. Published version in Comm. Math. Phys

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