标题： 无潮汐可穿越虫洞周围环绕着字符串云的$f(R)$引力 显示英文标题

标题： Tideless Traversable Wormholes surrounded by cloud of strings in $f(R)$ gravity

摘要： 我们研究了在$f(R)$引力度规形式下的无潮汐可穿越虫洞。 首先我们考虑了三种虫洞的形状函数并研究了它们的可行性与结构。 $f(R)$引力模型与虫洞形状函数之间的联系已被研究，$f(R)$引力模型与形状函数的依赖关系也已展示。 我们还得到了在$f(R)$引力 Starobinsky 模型中被字符串云包围的虫洞解。 在这种情况下，虫洞形状函数同时依赖于 Starobinsky 模型参数和字符串云参数。 虫洞的结构和高度受字符串云参数的影响很大，而对 Starobinsky 模型参数则不太敏感。 已经研究了能量条件，我们发现了所有虫洞结构的零能量条件违反范围。 使用高阶 WKB 近似方法研究了这些虫洞结构在标量和狄拉克扰动下的准正则模式。 对于玩具形状函数的准正则模式高度依赖于模型参数。 在 Starobinsky 模型的虫洞情况下，标量扰动中准正则频率和阻尼率随着 Starobinsky 模型参数的增加而增加。 而在狄拉克扰动中，随着 Starobinsky 模型参数的增加，准正则频率减少而阻尼率增加。 字符串云参数也显著且不同地影响着 Starobinsky 模型中虫洞的准正则模式。 显示英文摘要

摘要： We study the tideless traversable wormholes in the $f(R)$ gravity metric formalism. First we consider three shape functions of wormholes and study their viabilities and structures. The connection between the $f(R)$ gravity model and wormhole shape function has been studied and the dependency of the $f(R)$ gravity model with the shape function is shown. We also obtain a wormhole solution in the $f(R)$ gravity Starobinsky model surrounded by a cloud of strings. In this case, the wormhole shape function depends on both the Starobinsky model parameter and the cloud of strings parameter. The structure and height of the wormhole is highly affected by the cloud of strings parameter, while it is less sensitive to the Starobinsky model parameter. The energy conditions have been studied and we found the ranges of the null energy condition violation for all wormhole structures. The quasinormal modes from these wormhole structures for the scalar and Dirac perturbations are studied using higher order WKB approximation methods. The quasinormal modes for the toy shape functions depend highly on the model parameters. In case of the Starobinsky model's wormhole the quasinormal frequencies and the damping rate increase with an increase in the Starobinsky model parameter in scalar perturbation. Whereas in Dirac perturbation, with an increase in the Starobinsky model parameter the quasinormal frequencies decrease and the damping rate increases. The cloud of strings parameter also impacts prominently and differently the quasinormal modes from the wormhole in the Starobinsky model.