Calculus of Variations and Geometric Measure Theory

S. Almaraz - L. L. de Lima - L. Mari

Spacetime positive mass theorems for initial data sets with noncompact boundary

created by mari1 on 13 Dec 2020


Published Paper

Inserted: 13 dec 2020
Last Updated: 13 dec 2020

Journal: Int. Math. Res. Notices
Pages: 1-59
Year: 2020
Doi: 10.1093/imrn/rnaa226

ArXiv: 1907.02023 PDF


In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under suitable dominant energy conditions (DECs) imposed both on the interior and along the boundary, we prove the corresponding positive mass inequalities under the assumption that the underlying manifold is spin. In the asymptotically flat case, we also prove a rigidity statement when the energy-momentum vector is lightlike. Our treatment aims to underline both the common features and the differences between the asymptotically Euclidean and hyperbolic settings, especially regarding the boundary DECs.