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We provide a new proof of the equality case of the spacetime positive masstheorem, which states that if a complete asymptotically flat initial data set$(M, g, k)$ satisfying the dominant energy condition has null ADMenergy-momentum (that is, $|E|=|P|$), then $(M,g)$ must isometrically embedinto Minkowski space with $k$ as its second fundamental form. Previous proofseither used spinor methods [Wit 81, BC96, CM06], relied on the Jang equation[HL20, Eic13], or assumed three spatial dimensions [HZ22]. In contrast, our newproof only requires knowing that $E\ge|P|$ for all complete initial data setsnear $(g,k)$ on $M$ satisfying the dominant energy condition.

Equality in the spacetime positive mass theorem II