Ilka Rapp: Vanishing mass theorem

The case of vanishing mass for asymptotically flat spin manifolds \(M^n\) satisfying the dominant energy condition was categorized by Sven Hirsch and Yiyue Zhang in 2025. It was shown that, in the case of vanishing mass those manifolds \(M^n\) isometrically embed into pp-wave spacetimes. The idea behind the proof is to use the Positive mass theorem by Witten to construct a spacetime harmonic function, whose level sets model the planes of the pp-wave. The proof can be further used to show that in the special case where the manifold \(M^n\) has an interior MOTS or MITS boundary the mass can’t vanish.