Mathematics
The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets with Toroidal Infinity and Related Rigidity Results
Document Type
Article
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 et al. (Commun Math Phys 386(1):253–268, 2021) in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions.
Publication Title
Communications in Mathematical Physics
Publication Date
12-2022
Volume
396
Issue
2
First Page
451
Last Page
480
ISSN
0010-3616
DOI
10.1007/s00220-022-04467-x
Keywords
black holes, initial datum, manifold
Repository Citation
Alaee, Aghil; Hung, Pei Ken; and Khuri, Marcus, "The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets with Toroidal Infinity and Related Rigidity Results" (2022). Mathematics. 42.
https://commons.clarku.edu/mathematics/42
