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.