Equality in the Spacetime Positive Mass Theorem

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 $E=|P|$, then $E=|P|=0$, where $(E,P)$ 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.

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

References in corpus (1)

• The Higher Dimensional Positive Mass Theorem II

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• Spacetime Harmonic Functions and Applications to Mass
• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• Bartnik mass minimizing initial data sets and improvability of the dominant energy scalar
• Positive mass theorems for spin initial data sets with arbitrary ends and dominant energy shields
• Rigidity results for initial data sets satisfying the dominant energy condition
• On a spacetime positive mass theorem with corners
• Initial data sets with dominant energy condition admitting no smooth dec spacetime extension
• Hyperbolic positive energy theorems