Equality in the Spacetime Positive Mass Theorem
Differential Geometry
2019-11-27 v3
Abstract
We affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight. Namely, if an asymptotically flat initial data set satisfies the dominant energy condition and has , then , where is the ADM energy-momentum vector. The dimensional restriction can be removed if we assume the positive mass inequality holds. Previously the result was only known for spin manifolds.
Keywords
Cite
@article{arxiv.1706.03732,
title = {Equality in the Spacetime Positive Mass Theorem},
author = {Lan-Hsuan Huang and Dan A. Lee},
journal= {arXiv preprint arXiv:1706.03732},
year = {2019}
}
Comments
V2: New title, the proof of the Sobolev version of positive mass inequality (now Theorem 4.1) revised. V3: Elliptic regularity and the proof of Lemma 2.10 added in the appendices, upon referee's requests. Appeared in Comm. Math. Phys