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- Title
A Quasi-Local Mass.
- Authors
Alaee, Aghil; Khuri, Marcus; Yau, Shing-Tung
- Abstract
We define a new gauge independent quasi-local mass and energy, and show its relation to the Brown–York Hamilton–Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition. Like the Wang-Yau mass, the new definition relies on isometric embeddings into Minkowski space, although our notion of admissibility is different from that of Wang and Yau. Rigidity is also established, in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space, and conversely the mass vanishes for any such surface. Furthermore, we show convergence to the ADM mass at spatial infinity, and provide the equation associated with optimal isometric embedding.
- Subjects
MINKOWSKI space; HARMONIC functions; SPACETIME
- Publication
Communications in Mathematical Physics, 2024, Vol 405, Issue 5, p1
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-024-04976-x