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arXiv · 1907.02023

Spacetime positive mass theorems for initial data sets with noncompact boundary

Sergio Almaraz·Levi Lopes de Lima·Luciano Mari
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Abstract

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.

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Sergio Almaraz, Levi Lopes de Lima, Luciano Mari. 2020-11-15. Spacetime positive mass theorems for initial data sets with noncompact boundary. https://doi.org/10.1093/imrn%2Frnaa226

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