Initial data set rigidity results for polyhedra

2024/08/25 by Chai, Xiaoxiang, Wan, Xueyuan
#53C24 #53C27 #83C05 #83C60 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2408.13801

Abstract

Using spinors, we show a dihedral type rigidity for polyhedral initial data sets. This rigidity connects spacetime positive mass theorem, dihedral rigidity and capillary marginally trapped surfaces. Our method is to extend the rigidity analysis of spacetime positive mass theorem due to Beig-Chrusciel to the settings of a twisted spinor bundle.

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