Quasi-local energy and the choice of reference
Quasi-local energy and the choice of reference
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DOI：
10.1088/0264-9381/28/19/195019
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发表时间：
2011-05
影响因子：
3.5
通讯作者：
Jian-Liang Liu;Chiang-Mei Chen;J. M. Nester
中科院分区：
文献类型：
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作者：
Jian-Liang Liu;Chiang-Mei Chen;J. M. Nester
爱因斯坦广义相对论的准局部能量是由协变哈密顿形式中首选边界项的值来定义的。边界项取决于参考点的选择和区域边界上的类时位移向量场（可以与观察者相关联）。这里，我们分析了球对称情况。对于明显的基于度量分量的参考点解析选择，我们发现该方法在几种标准坐标系下给出相同的准局部能量值，而在其他一些坐标系下可以给出不同的值。对于均匀各向同性宇宙论，能量可以是非正的，一种情况是平坦空间的能量是负的。作为一种替代方案，我们引入了一种通过极值能量来确定参考点和位移的选择的方法。这个过程给出了不同坐标系下史瓦西空间能量的相同值，以及宇宙模型的非负值，动态宇宙学的能量为零实际上是闵可夫斯基空间。类时位移矢量是两边界的对偶平均曲率矢量。
A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector field (which can be associated with an observer) on the boundary of the region. Here, we analyze the spherical symmetric cases. For the obvious analytic choice of reference based on the metric components, we find that this technique gives the same quasi-local energy values using several standard coordinate systems and yet can give different values in some other coordinate systems. For the homogeneous-isotropic cosmologies, the energy can be non-positive, and one case which is actually flat space has a negative energy. As an alternative, we introduce a way to determine the choice of both the reference and displacement by extremizing the energy. This procedure gives the same value for the energy in different coordinate systems for the Schwarzschild space, and a non-negative value for the cosmological models, with zero energy for the dynamic cosmology which is actually Minkowski space. The time-like displacement vector comes out to be the dual mean curvature vector of the two-boundary.