论文标题
球形壳的高斯曲率：复杂性的几何测量
Gaussian curvature of spherical shells: A geometric measure of complexity
论文作者
论文摘要
在本文中，我们考虑了球形对称的空间的半元素协变量分解，并找到了由于分解而出现的二维球形壳的高斯曲率的高斯曲率的副曲线方程。该双曲线方程的恢复因子使我们能够构建复杂性的几何度量。该措施批判性地取决于高斯曲率，我们首次证明了与复杂性的几何连接。我们通过对具有不同物质分布的众所周知的球形对称指标进行分类来说明该度量的实用性。我们还根据所有球形对称空间的集合，根据它们的复杂性和物理特性来定义一个顺序结构。
In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find a governing hyperbolic equation of the Gaussian curvature of two dimensional spherical shells, that emerges due to the decomposition. The restoration factor of this hyperbolic travelling wave equation allows us to construct a geometric measure of complexity. This measure depends critically on the Gaussian curvature, and we demonstrate this geometric connection to complexity for the first time. We illustrate the utility of this measure by classifying well known spherically symmetric metrics with different matter distributions. We also define an order structure on the set of all spherically symmetric spacetimes, according to their complexity and physical properties.
