Density and positive mass theorems for initial data sets with boundary. (English) Zbl 1510.83017
Summary: 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.
MSC:
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 11R45 | Density theorems |
| 58J47 | Propagation of singularities; initial value problems on manifolds |
| 14B25 | Local structure of morphisms in algebraic geometry: étale, flat, etc. |
| 47A10 | Spectrum, resolvent |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
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