Scalar Field Kantowski–Sachs Solutions in Teleparallel F(T) Gravity - Alexandre Landry (Universe)
In this paper, we investigate time-dependent Kantowski–Sachs spherically symmetric teleparallel <semantics>F(T)</semantics> gravity with a scalar field source. We begin by setting the exact field equations to be solved and solve conservation laws for possible scalar field potential, <semantics>V<mfenced open="(" close=")">ϕ</mfenced></semantics>, solutions. Then, we find new non-trivial teleparallel <semantics>F(T)</semantics> solutions by using power-law and exponential ansatz for each potential case arising from conservation laws, such as linear, quadratic, or logarithmic, to name a few. We find a general formula allowing us to compute all possible new teleparallel <semantics>F(T)</semantics> solutions applicable for any scalar field potential and ansatz. Then, we apply this formula and find a large number of exact and approximate new teleparallel <semantics>F(T)</semantics> solutions for several types of cases. Some new <semantics>F(T)</semantics> solution classes may be relevant for future cosmological applications, especially concerning dark matter, dark energy quintessence, phantom energy leading to the Big Rip event, and quintom models of physical processes.