$f(T)$ 引力中Padé近似虫洞的光学与动力学特征
Optical and Dynamical Signatures of Padé Approximated Wormholes in $f(T)$ Gravity
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中文总结 AI 辅助
本研究在$f(T)$引力中构建两种Padé近似虫洞，验证其物理可行性，并通过光学观测特征与动力学稳定性分析，揭示其可观测信号与稳定性差异。
中文摘要 AI 辅助
我们在线性远距平行模型 $f(T) = \alpha T + \beta$ 中构建了可穿越虫洞解，采用 [1/0] 和 [0/1] 阶的Padé近似作为形状函数，并采用红移函数 $\Phi(r) = -M/r$，从修正场方程中推导出相应的源项。我们通过能量条件、Tolman--Oppenheimer--Volkoff平衡、体积积分量化器、与外部Schwarzschild真空的薄壳匹配、嵌入图、固有径向距离、引力能量和活跃质量来评估两种构型的物理可行性。然后，我们通过分析赤道零测地线和光子球结构、计算阴影图和径向强度分布、对几何薄吸积盘的相对论图像进行光线追踪，并积分类时玫瑰轨道，来检验每种几何的观测特征。最后，我们通过三阶WKB准正则模分析，在标量、电磁和轴向引力扰动下研究两种虫洞的动力学稳定性，并与时域演化和eikonal光子球对应进行交叉验证，同时考察模谱的参数依赖性以及束缚模回波的可能性。
英文摘要
We construct traversable wormhole solutions in the linear teleparallel model $f(T) = αT + β$, adopting Padé approximants of order [1/0] and [0/1] as shape functions together with the redshift function $Φ(r) = -M/r$, and derive the corresponding source terms from the modified field equations. We assess the physical viability of both configurations through the energy conditions, Tolman--Oppenheimer--Volkoff equilibrium, the volume integral quantifier, thin-shell junction matching to an exterior Schwarzschild vacuum, embedding diagrams, proper radial distance, the gravitational energy and the active mass. We then examine the observational signatures of each geometry by analysing equatorial null geodesics and the photon-sphere structure, computing shadow maps and radial intensity profiles, ray-tracing relativistic images of a geometrically thin accretion disc, and integrating timelike rosette orbits. Finally, we study the dynamical stability of both wormholes through a third-order WKB quasinormal-mode analysis across scalar, electromagnetic, and axial gravitational perturbations, cross-checked against time-domain evolution and the eikonal photon-sphere correspondence, and examine the parameter dependence of the mode spectrum together with the possibility of trapped-mode echoes.
发表机构
- Chennai Mathematical Institute（金奈数学研究所）
- Birla Institute of Technology and Science, Pilani, Hyderabad Campus（比拉理工学院，皮拉尼校区，海德拉巴分校）
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