Positive mass theorem for initial data sets with corners along a hypersurface

2019/06/20 by Aghil Alaee, Shing–Tung Yau, Alaee, Aghil +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.1906.08796

openalex publication_date 2019/06/20 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein) asymptotically flat or asymptotically cylindrical, for 4-dimensional Einstein-Maxwell theory and 5-dimensional minimal supergravity theory which metrics fail to be C¹ and second fundamental forms and electromagnetic fields fail to be C⁰ across an axially symmetric hypersurface Σ. Furthermore, we remove the completeness and simple connectivity assumptions in this result and prove it for manifold with boundary such that the mean curvature of the boundary is non-positive.

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