We propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with positive intrinsic curvature in a spacetime. Our definitions do not depend on the compact spacelike hypersurface it bounds. We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface.
@inproceedings{chiu-chu2003new,
title={New definition of quasilocal mass and its positivity},
author={Chiu-Chu Melissa Liu, and Shing-Tung Yau},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204747404751217},
year={2003},
}
Chiu-Chu Melissa Liu, and Shing-Tung Yau. New definition of quasilocal mass and its positivity. 2003. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204747404751217.