TY - JOUR

T1 - Quasi-local energy for spherically symmetric spacetimes

AU - Wu, Ming Fan

AU - Chen, Chiang Mei

AU - Liu, Jian Liang

AU - Nester, James M.

N1 - Funding Information:
Acknowledgments We much appreciated several good suggestions from the referees which led to significant improvements. This work was supported by the National Science Council of the R.O.C. under the grants NSC-99-2112-M-008-004, NSC-100-2119-M-008-018 (JMN) and NSC 99-2112-M-008-005-MY3 (CMC) and in part by the National Center of Theoretical Sciences (NCTS).

PY - 2012/9

Y1 - 2012/9

N2 - 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.

AB - 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.

KW - Hamiltonian boundary term

KW - Quasi-local energy

KW - Spherically symmetric spacetimes

UR - http://www.scopus.com/inward/record.url?scp=84865427181&partnerID=8YFLogxK

U2 - 10.1007/s10714-012-1399-3

DO - 10.1007/s10714-012-1399-3

M3 - 期刊論文

AN - SCOPUS:84865427181

SN - 0001-7701

VL - 44

SP - 2401

EP - 2417

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

IS - 9

ER -