Angular momentum and an invariant quasilocal energy in general relativity
Angular momentum and an invariant quasilocal energy in general relativity
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DOI：
10.1103/physrevd.62.124018
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发表时间：
2000-03
影响因子：
5
通讯作者：
R. Epp
中科院分区：
文献类型：
--
作者：
R. Epp
由于布朗-约克准定域能面密度在局域助推下的变换性质，它与狭义相对论公式中的E类似：E^2-p^2=m^2。在本文中，我将激发这个公式的广义相对论版本，从而得出“不变准定域能量”或IQE的几何自然定义。与不变质量m类似，IQE在时空中给定的两面S上的观测者集合的局部提升下是不变的。需要一个参考能量减法程序，但与布朗-约克程序相反，S等距嵌入四维参考时空。这实际上消除了使用三维参考空间所固有的嵌入性问题，但引入了一个新的问题：这种嵌入不是唯一的，导致参考IQE中的模糊性。然而，在这个余维2的设置中，有两个曲率与S相关联：它的切线束和法向束的曲率。利用这一事实，我将提出一种可能的方法来解决嵌入的歧义，这在同一时间将被视为纳入角动量的能量在准局域水平。我将在以下情况下分析IQE：在渐近平坦时空中的大球体的空间和未来的零无限极限;沿着空间或零方向向一点收缩的小球体;最后，在渐近反德西特时空中。最后一种情况下，揭示了一个惊人的相似性之间的参考IQE和最近提出的一定的counterterm能源的背景下，adtured的AdS/CFT对应。
Owing to its transformation property under local boosts, the Brown-York quasilocal energy surface density is the analogue of E in the special relativity formula: E^2-p^2=m^2. In this paper I will motivate the general relativistic version of this formula, and thereby arrive at a geometrically natural definition of an `invariant quasilocal energy', or IQE. In analogy with the invariant mass m, the IQE is invariant under local boosts of the set of observers on a given two-surface S in spacetime. A reference energy subtraction procedure is required, but in contrast to the Brown-York procedure, S is isometrically embedded into a four-dimensional reference spacetime. This virtually eliminates the embeddability problem inherent in the use of a three-dimensional reference space, but introduces a new one: such embeddings are not unique, leading to an ambiguity in the reference IQE. However, in this codimension-two setting there are two curvatures associated with S: the curvatures of its tangent and normal bundles. Taking advantage of this fact, I will suggest a possible way to resolve the embedding ambiguity, which at the same time will be seen to incorporate angular momentum into the energy at the quasilocal level. I will analyze the IQE in the following cases: both the spatial and future null infinity limits of a large sphere in asymptotically flat spacetimes; a small sphere shrinking toward a point along either spatial or null directions; and finally, in asymptotically anti-de Sitter spacetimes. The last case reveals a striking similarity between the reference IQE and a certain counterterm energy recently proposed in the context of the conjectured AdS/CFT correspondence.