The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results
arXiv:2201.04327 · doi:10.1007/s00220-022-04467-x
Abstract
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the umbilic case, a rigidity statement is proven showing that the total energy vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes [10] in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions.
arXiv comment28 pages, final version
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