论文标题
在圆柱上对称时空中的四维小说和正则EGB理论之间的解决方案的等效性
Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime
论文作者
论文摘要
最近，提出了一种新型的四维爱因斯坦 - 加斯 - 鲍内特（EGB）理论，以绕过Lovelock定理，并对四维局部重力产生非平凡的影响。主要机制是引入重新定义$α\rightarrowα/（d-4）$，并采用限制$ d \ rightarrow4 $。但是，该理论没有标准的四维场方程。然后提出一些正规化程序来解决此问题[ARXIV：2003.11552，ARXIV：2003.12771，ARXIV：2004.08362，ARXIV：2004.09472，ARXIV：2004.10716]。所得正规化的四维EGB理论具有与原始理论相同的壳作用。因此，预计新颖的四维EGB理论等同于其正则化版本。但是，这两种理论的等效性是对称依赖性的。在本文中，我们测试了圆柱对称时空中的等效性。获得了这两种理论的定义明确的场方程，我们的后续分析表明它们在这种时空中是等效的。然后，圆柱形宇宙弦被视为度量的特定示例。获得了三组溶液，并评估了相应的丝质量密度。结果揭示了高斯 - 骨网中如何在四个维度上有助于新理论中的字符串几何形状。
Recently, a novel four-dimensional Einstein-Gauss-Bonnet (EGB) theory was presented to bypass the Lovelock's theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $α\rightarrowα/(D-4)$ and to take the limit $D\rightarrow4$. However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem [arXiv:2003.11552, arXiv:2003.12771, arXiv:2004.08362, arXiv:2004.09472, arXiv:2004.10716]. The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss-Bonnet term in four dimensions contributes to the string geometry in the new theory.
