论文标题
分布3+1泡沫模型的经典方面
Classical Aspects of a Distributional 3+1 Foam Model
论文作者
论文摘要
引入了3+1个时空，带有移位矢量，是线性化波算子的独特基本解决方案，以建模对Wheeler Layman的量子泡沫类比的解释。要了解该模型的分布方面是保证存在一系列紧凑型移位矢量的序列，该偏移向量收敛到用于引入3+1个全球双曲线序列序列的基本解决方案。使用这些因果稳定的空间的序列，表明存在一个正整数，因此，对于序列中的所有元素，索引值都比该整数更高，对于任何欧拉尔观察者而言，移位矢量的增加都会比任何多种元素都更快地增加，并且体积扩展比所有方向都更快。对于外部曲率的痕迹，相同的结论仍然有效。尽管如此，无论这些元素的外在曲率有多大挥发性，在序列的另一端，外部曲率可忽略不计和时空平坦的元素。
A 3+1 spacetime, with a shift vector that is the unique fundamental solution to the linearized wave operator, is introduced to model an interpretation of Wheeler's layman's analogy of the Quantum foam. To understand the distributional aspects of this model is the guaranteed existence of a sequence of compactly supported shift vectors that converge to the fundamental solution used to introduce a sequence of 3+1 globally hyperbolic spacetimes. Using the sequence of these causally stable spacetimes it is shown that there exists a positive integer such that for all elements in the sequence with a greater index value than this integer and for any Eulerian observer will the shift vector increase more rapidly than any polynomial and the volume expansion is more rapid than a polynomial in all directions. The same conclusion remains valid for the trace of the extrinsic curvature. Nonetheless, it is shown, no matter how volatile the extrinsic curvature is for these elements there also exists elements in the other end of the sequence where the extrinsic curvature is negligible and the spacetime flat.
