摘要： We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime. 其他題名： Gen Relativ Gravit 出版者： Boston: Springer US 出版日期： 2012-09 出處： General relativity and gravitation, 2012-09, Vol.44 (9), p.2401-2417 資源來源： SpringerLink Journals - AutoHoldings 版權： Springer Science+Business Media, LLC 2012 識別號： ISSN: 0001-7701 識別號： EISSN: 1572-9532 識別號： DOI: 10.1007/s10714-012-1399-3
