Equality in the spacetime positive mass theorem

The equality case of the spacetime positive mass theorem says that an asymptotically flat initial data set with the dominant energy condition and the null ADM energy-momentum must isometrically embed into Minkowski space. Previous proofs either used spinor methods, relied on the Jang equation, or assumed three spatial dimensions. We provide a new proof using the variational property of a family of modified Regge-Teitelboim functionals. Counterexamples in higher dimensions will also be discussed. This talk is based on joint work with Dan Lee.