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 (Beig and Chruściel in J Math Phys37(4):1939–1961, 1996; Chruściel and Maerten in J Math Phys 47(2), 2006).