Kantowski-Sachs spherically symmetric solutions in teleparallel $F(T)$ gravity

In this paper, we investigate time-dependent spherically symmetric Kantowski-Sachs teleparallel $F(T)$ gravity in vacuum and in a perfect isotropic fluid. We first find the field equations and solve for new teleparallel $F(T)$ solutions. By using a power-law ansatz for the coframe functions, we find some new non-trivial teleparallel $F(T)$ vacuum solutions. We then proceed to find new non-trivial teleparallel $F(T)$ solutions in a perfect isotropic fluid with both linear and non-linear equation of state. We find several new exact and approximate teleparallel $F(T)$ solutions. These classes of new solutions are relevant for future cosmological applications.