The limiting behavior of the Liu-Yau quasi-local energy
The limiting behavior of the Liu-Yau quasi-local energy
复制标题
刘丘准局部能量的限制行为
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
P. Yu
中科院分区：
文献类型：
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作者：
P. Yu
最近提出的准局域能量的小和大球的限制，刘和丘仔细检查。结果表明，在小球极限下，Liu-Yau准局域能的非真空极限接近于期望值frac {4 pi}{3} r^3 T（e_0，e_0）$。这里T是物质的能量应力张量，T_pM中的e_0是类时的，指向极限r中半径为r的小球的中心点p 0 0。然而在真空中，Liu-Yau准局域能的极限值包含期望的极限分数{r^5}{90} B（e_0，e_0，e_0，e_0），其中B是Bel-Robinson张量，以及一个额外的项。在零无穷大的大球极限下，对于孤立的引力源，Liu-Yau准局域能量被证明可以恢复Bondi质量和Bondi news通量，时空在零无穷大是渐近空的和平坦的。根据这些结果讨论了Liu-Yau模型的物理有效性。
The small- and large-sphere limits of the quasi-local energy recently proposed by Liu and Yau are carefully examined. It is shown that in the small-sphere limit, the non-vacuum limit of the Liu-Yau quasi-local energy approaches the expected value frac{4pi}{3} r^3 T(e_0, e_0)$. Here, T is the energy-stress tensor of matter, e_0 in T_p M is unit time-like and future-directed at the point p located at the center of the small sphere of radius $r$ in the limit r o 0. In vacuum, however, the limiting value of the Liu-Yau quasi-local energy contains the desired limit frac{r^5}{90} B(e_0, e_0, e_0, e_0), where B is the Bel-Robinson tensor, as well as an extra term. In the large-sphere limit at null infinity, for isolated gravitational sources, the Liu-Yau quasi-local energy is shown to recover the Bondi mass and Bondi news flux, in space-times that are asymptotically empty and flat at null infinity. The physical validity of the Liu-Yau model in view of these results is discussed.