$f(T)$ Corrected Instability of Cylindrical Collapsing Object with Harrison-Wheeler Equation of State

In this paper, we study the dynamical instability of a collapsing object in the framework of generalized teleparallel gravity. We assume a cylindrical object with a specific matter distribution. This distribution contains energy density, isotropic pressure component with heat conduction. We take oscillating states scheme up to first order to check the instable behavior of the object. We construct a general collapse equation for underlying case with non-diagonal tetrad depending on the matter, metric functions, heat conducting term and torsional terms. The Harrison-Wheeler equation of state which contains adiabatic index is used to explore the dynamical instability ranges for Newtonian and post-Newtonian constraints. These ranges depend on perturbed part of metric coefficients, matter parts and torsion.