We present version v59.0 of the Karahan Framework, extending the minimal nonlinear teleparallel gravity model F(T)=T+ξT² toward axisymmetric configurations. Building on the previously established spherically symmetric, regularized compact-object solution, we introduce a minimal off-diagonal geometric term that captures the effect of localized, vortex-like torsion structures in the exterior region of compact objects. This extension preserves the General Relativity limit while incorporating a single anisotropic degree of freedom consistent with Ockham’s razor. Within this framework, null geodesics are modified through the induced coupling between temporal and azimuthal directions, leading to direction-dependent photon trajectories. As a result, the black hole shadow is no longer strictly circular but exhibits controlled deviations in both size and shape. The proposed ansatz is not claimed as an exact solution of the full F(T) field equations but rather as a mathematically consistent and physically motivated minimal extension that translates torsion-induced vortex structures into observable signatures. This formulation establishes a direct link between torsion geometry and black hole imaging, providing a testable pathway for probing deviations from standard gravity in high-resolution observational data.
Asil Karahan (Thu,) studied this question.