超双曲虫洞几何及其形变研究
On Super-Hyperbolic Wormhole Geometries and their Deformations
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中文总结 AI 辅助
本研究建立了超双曲形变构造可穿越虫洞的几何与相对论框架，推导了相关解析表达式与稳定性判据，为广义相对论中奇异几何探索提供了新途径。
中文摘要 AI 辅助
本研究针对一类由经典悬链面经超双曲形变构造的可穿越虫洞，建立了统一的几何与相对论框架。该几何嵌入结合了确保规则喉道的显式局部曲率参数κ，以及基于Mittag-Leffler的超双曲面形变函数𝔖C_α(v)，其中形变参数α>1控制喉道之外嵌入的径向起始位置与远场增长，在边界极限α→1⁺时连续趋近经典悬链面几何。通过引入非恒定红移Φ(r)，系统推导了形状函数、曲率张量、物质源与连接条件的闭式解析表达式，最终得到精确的薄壳运动方程与稳定性判据。本工作为虫洞理论的扩展建立了数学自洽且物理可行的框架，为广义相对论中奇异几何的探索提供了新途径，并明确了可穿越构型保持局域稳定的条件。
英文摘要
In this study, we developed a unified geometric and relativistic framework for a new family of traversable wormholes constructed from a super-hyperbolic deformation of the classical catenoid, whose geometric embedding combines an explicit local curvature parameter $κ$, which secures a regular throat, with the Mittag-Leffler-based super-hyperboloid deformation function ${\mathfrak{S}C}_α (v)$, where the deformation parameter $α>1$ governs the radial onset and far-field growth of the embedding beyond the throat, continuously approaching the classical catenoidal geometry in the boundary limit $α\rightarrow1^{+}$. Allowing a non-constant redshift $Φ(r)$, we systematically evaluate closed analytical expressions for the shape function, curvature tensors, matter sources, and junction conditions, culminating in an exact thin-shell equation of motion and stability criterion. This work establishes a mathematically consistent and physically viable framework for the extension of wormhole theory, providing a new avenue for exploring exotic geometries within general relativity and identifying the conditions under which traversable configurations remain locally stable.
