AI 中文总结
研究遥平行\(F(T)\)引力中康德owski - Sachs几何结构，用余标架 - 自旋联络等方法，由查普利金型和多方态流体源产生的守恒定律重构\(F(T)\)，有幂律和指数分支，给出局部各向异性宇宙学等解释，颠倒标准重构策略。
AI 中文摘要
利用余标架 - 自旋联络形式和不变的科利 - 兰德里方法，为遥平行\(F(T)\)引力中由查普利金型和多方态流体源产生的康德owski - Sachs（KS）几何结构开发了一个协变重构框架。物质部分由非线性状态方程建模，包括广义查普利金气体\(p = -A / \rho^{\alpha}\)和多方态定律\(p = K\rho^{\Gamma}\)。相应的守恒定律确定了流体密度对各向异性KS体积\(V = A_2A_3^2\)的依赖性。然后将这些源标度插入协变遥平行场方程的对称部分，并用于直接从KS动力学重构\(F(T)\)的函数形式。幂律和指数假设产生不同的不变重构分支。在幂律部分，查普利金流体产生混合的常数加幂源项，而多方态部分产生由多方态指数控制的密度幂。在指数部分，自然重构变量是移位不变量\(X = T_0 - T\)，导致移位的遥平行德西特分支。重构模型被解释为局部各向异性宇宙学部分，对于收缩的角KS尺度因子，被解释为局部康德owski - Sachs黑洞内部重构分支。分析是局部的且依赖于分支；通过\(F_T>0\)和\(F_{TT}>0\)评估领先阶可行性，而完整的微扰稳定性分析留待未来工作。重构完全由非线性物质守恒定律驱动，从而颠倒了先验规定引力拉格朗日量的标准重构策略。
英文摘要
A covariant reconstruction framework for Kantowski--Sachs (KS) geometries sourced by Chaplygin-type and polytropic fluids in teleparallel $F(T)$ gravity is developed using the coframe--spin-connection formalism and the teleparallel invariant approach. The matter sector is modelled by nonlinear equations of state, including the generalized Chaplygin gas $p=-A/ρ^α$ and a polytropic law $p=Kρ^Γ$. The corresponding conservation laws determine the dependence of the fluid density on the anisotropic KS volume $V=A_2A_3^2$. These source scalings are then inserted into the symmetric part of the covariant teleparallel field equations and used to reconstruct the functional form of $F(T)$ directly from the KS dynamics. Power-law and exponential ansätze generate distinct invariant reconstruction branches. In the power-law sector, the Chaplygin fluid produces mixed constant-plus-power source terms, while the polytropic sector generates density powers controlled by the polytropic index. In the exponential sector, the natural reconstruction variable is the shifted invariant $X=T_0-T$, leading to shifted teleparallel de Sitter branches. The reconstructed models are interpreted as local anisotropic cosmological sectors and, for contracting angular KS scale factors, as local Kantowski--Sachs black-hole-interior reconstruction branches. The analysis is local and branch-dependent; leading-order viability is assessed through \(F_T>0\) and \(F_{TT}>0\), while a complete perturbative stability analysis is left for future work. The reconstruction is entirely driven by nonlinear matter conservation laws, thereby reversing the standard reconstruction strategy in which the gravitational Lagrangian is prescribed a priori.
Comments14 pages, no figure
