Hamiltonian boundary term and quasilocal energy flux
Hamiltonian boundary term and quasilocal energy flux
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DOI：
10.1103/physrevd.72.104020
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发表时间：
2005-08
影响因子：
5
通讯作者：
Chiang-Mei Chen;J. M. Nester;R. Tung
中科院分区：
文献类型：
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作者：
Chiang-Mei Chen;J. M. Nester;R. Tung
引力区域的哈密顿量包含一个边界项，该边界项不仅决定拟局部值，而且通过边界变分原理决定边界条件。利用协变哈密顿公式，我们得到了四种特定的准局部能量-动量边界项表达式；每个都对应一个物理上不同的和几何上清晰的边界条件。这里，从渐近的考虑出发，我们展示了一个基本哈密顿恒等式如何自然地导致相关的准局部能量通量表达式。对于电磁学来说，四种中的一种是有区别的：唯一一种是规范不变的；它给出了我们熟悉的能量密度和波印廷通量。对于爱因斯坦的广义相对论，两种不同的边界条件选择对应于准局部表达式，这些准局部表达式渐近地给出ADM能量、Trautman-Bondi能量以及相关的能量通量（输出和输入）。这里还有一个特别的表达式协变的表达式。
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant.