从引力作用量中的准局域能量项提取动力学自由度
Extracting Dynamical Degrees of Freedom From the Quasi-Local Energy Term in the Gravitational Action
AI总结：
本文证明在适当条件下，广义相对论的动力学内容可存储于Brown-York准局域能量项中，并据此推导出时间-能量型不确定性关系，可能有助于理解引力诱导的量子态坍缩及黑洞辐射。
摘要：
本文证明，在适当的坐标系统及合适的时间切片下，若满足适当条件，则在没有物质的情况下，哈密顿量与包含所有必要边界项的Einstein-Hilbert作用量可以在壳上以Brown-York准局域能量的形式写出。若存在物质，则非零的体项仅由应力-能量张量构成。文中论证，广义相对论的动力学内容存储于准局域能量项中。这一结果强调了将Brown-York准局域能量解释为引力场的场能量加上应力-能量的观点。作为应用，我们推导了时间-能量型的不确定性关系，这可能有助于理解引力诱导的量子态坍缩，以及更常规的共轭变量间的不确定性关系。后者针对一个修正的Vaidya度规进行计算，该度规可用于研究黑洞辐射。以准局域能量表示的边界项抵消了作用量中的二阶导数项，在所选择的规范下仅留下一个一阶导数项的平方，这对于作用量的量子化是理想的。
英文摘要：
It is shown that under proper conditions in an appropriate coordinate system with a suitable time slicing the Hamiltonian and the Einstein-Hilbert action including all necessary boundary terms can be written on shell in terms of the Brown-York quasi-local energy in the absence of matter. If matter is present the non-vanishing bulk term only consists of stress-energy. It is argued that the dynamical content of general relativity is stored in the quasi-local energy term. The results underscore the interpretation of the Brown-York quasi-local energy as the field energy of the gravitational field plus stress-energy. As an application we derive uncertainty relations of the time-energy kind which may be useful in the understanding of gravity induced quantum state reduction and the more conventional kind for conjugate variables. The latter is computed for a modified Vaidya metric which may be used in the investigation of black hole radiance. The boundary terms expressed as quasi-local energy cancel second derivatives in the action leaving only a square of a first derivative term in the chosen gauge which is desirable for a quantization of the action.
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