具有全局背景结构的高维键能
Higher Dimensional Bondi Energy with a Globally Specified Background Structure
摘要：
最近，gr-qc/0304054在共形无穷大和哈密顿形式化的框架内提出了更高维（偶时空）的Bondi能量的推广。然而，在gr-qc/0304054中用来推导邦迪能量表达式的规范条件是特殊的，因为该规范所指定的零无穷大截面是各向异性的，实际上是非紧的。因此，在一般渐近平坦的辐射时空中，这个规范很难用于明确计算邦迪能量。在这种规范条件下，我们也不清楚高维和四维的Bondi能量表达式之间的明显差异是由于规范的选择，还是由于高维引力和四维引力的性质不同。在本文中，我们认为，高斯零共形规范作为一个更自然的规范条件，承认一个全球规范的背景结构与紧凑，球形横截面的零无穷大。相应地，我们修改了以前高维新闻张量的定义，使它在高斯零共形规范中得到了很好的定义，并推导出真空解的新规范选择中的邦迪能量-动量表达式，它在大于或等于4的任意（甚至时空）维中具有普遍形式。
英文摘要：
A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed by gr-qc/0304054 within the framework of conformal infinity and Hamiltonian formalizm. The gauge condition employed in gr-qc/0304054 to derive the Bondi energy expression is, however, peculiar in the sense that cross-sections of null infinity specified by that gauge are anisotropic and in fact non-compact. For this reason, that gauge is difficult to use for explicit computations of the Bondi energy in general, asymptotically flat radiative spacetimes. Also it is not clear, under that gauge condition, whether apparent difference between the expressions of higher dimensional Bondi energy and the 4-dimensional one is due to the choice of gauges or qualitatively different nature of higher dimensional gravity from 4-dimensional gravity. In this paper, we consider instead, Gaussian null conformal gauge as one of more natural gauge conditions that admit a global specification of background structure with compact, spherical cross-sections of null infinity. Accordingly, we modify the previous definition of higher dimensional news tensor so that it becomes well-defined in the Gaussian null conformal gauge and derive, for vacuum solutions, the expression for the Bondi energy-momentum in the new gauge choice, which takes a universal form in arbitrary (even spacetime) dimensions greater than or equal to four.
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