论文标题
爱因斯坦 - 希尔伯特作用的新型探测：度量参数的动态升级
A novel probe of Einstein-Hilbert action: Dynamic upgradation of metric parameters
论文作者
论文摘要
爱因斯坦 - 希尔伯特（EH）的行动在许多方面都是奇特的。文学中已经突出了一些特殊的特征。在本文中，我们讨论了EH动作的一些特殊特征，这些特征尚未在之前讨论过。众所周知，有几种方法将EH动作分解为批量和表面部分，并具有不同的潜在动机。我们对所有这些分解进行了审查。然后，我们试图通过恒定度量参数的动态升级来研究静态坐标作为时间相关坐标的限制情况。首先，我们研究了存在静态和球形对称（SSS）度量的恒定参数被促进到时间依赖变量时的后果，这使我们能够将时间依赖性纳入静态坐标。我们发现，在每组分解中，批量项的表达仍然不变，而表面项则随着总导数项而变化。最后，当我们消除公制参数的时间依赖性时，我们发现ricci-scalar（或EH动作）的表达不会返回其原始值。取而代之的是，我们发现曲率在地平线上变得奇异，这意味着与原始时空发生了拓扑变化。
The Einstein-Hilbert (EH) action is peculiar in many ways. Some of the Peculiar features have already been highlighted in literature. In the present article, we have discussed some peculiar features of EH action which has not been discussed earlier. It is well-known that there are several ways of decomposing the EH action into the bulk and the surface part with different underlying motivations. We provide a review on all of these decompositions. Then, we attempt to study the static coordinate as a limiting case of a time-dependent coordinate via dynamic upgradation of the constant metric parameters. Firstly, we study the consequences when the constant parameters, present in a static and spherically symmetric (SSS) metric, are promoted to the time dependent variables, which allows us to incorporate the time-dependence in the static coordinate. We find that, in every sets of decomposition, the expression of the bulk term remains invariant, whereas the surface term changes by a total derivative term. Finally, when we obliterate the time dependence of the metric parameters, we find that the expression of the Ricci-scalar (or the EH action) does not go back to its original value. Instead, we find that the curvature becomes singular on the horizon, which implies a topological change from the original spacetime.
