Electromagnetic Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity

Abstract

A covariant reconstruction framework for electromagnetic Kantowski--Sachs (KS) geometries in teleparallel $F(T)$ gravity is developed using the coframe/spin-connection (CSC) formalism and the invariant approach. In a restricted Maxwell-compatible branch, the electromagnetic conservation laws strongly constrain the anisotropic KS scale factors and lead to the scaling ${\rho }_{\mathrm{em}}\propto A_3^{-4}$. The corresponding symmetric and antisymmetric field equations are derived 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 associated with electric, magnetic, and transverse electromagnetic sectors. The exponential branch naturally admits reduced teleparallel de Sitter limits and shifted models of the form $F(T)=f(T_0-T)$. The reconstructed branches describe anisotropic cosmological sectors together with local BH-interior-like sectors that may reproduce reduced BH-interior-like or RN--dS-type behaviors at the level of the KS dynamics. These branches are organized through the invariant coframe/spin-connection classification and screened using the necessary leading-order viability conditions $F_T>0$ and $F_{TT}>0$. The local and branch-dependent nature of the construction is emphasized throughout.

19 pages, no figure. Published in Symmetry

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