Kantowski–Sachs Spherically Symmetric Solutions in Teleparallel F(T) Gravity

In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel $F\left(T\right)$ gravity in vacuum and in a perfect isotropic fluid. We begin by finding the field equations and solve for new teleparallel $F\left(T\right)$ solutions. With a power-law ansatz for the co-frame functions, we find new non-trivial teleparallel $F\left(T\right)$ vacuum solutions. We then proceed to find new non-trivial teleparallel $F\left(T\right)$ solutions in a perfect isotropic fluid with both linear and non-linear equations of state. We find a great number of new exact and approximated teleparallel $F\left(T\right)$ solutions. These classes of new solutions are relevant for future cosmological applications.