The case of equality for the spacetime positive mass theorem

DOI10.1007/S12220-022-01060-5arXiv2203.01984MaRDI QIDQ6392737

Sven Hirsch, Yiyue Zhang

Publication date: 3 March 2022

Abstract: The rigidity of the spacetime positive mass theorem states that an initial data set $(M,g,k)$ satisfying the dominant energy condition with vanishing mass can be isometrically embedded into Minkowski space. This has been established by Beig-Chru'sciel and Huang-Lee under additional decay assumptions for the energy and momentum densities $mu$ and $J$. In this note we give a new and elementary proof in dimension 3 which removes these additional decay assumptions. Our argument uses spacetime harmonic functions and Liouville's theorem. We also provide an alternative proof based on the Killing development of $(M,g,k)$.

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

This page was built for publication: The case of equality for the spacetime positive mass theorem

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6392737)