Scalar Field Kantowski--Sachs Solutions in Teleparallel $F(T)$ Gravity

TL;DR

The paper addresses Kantowski--Sachs spacetimes in covariant teleparallel $F(T)$ gravity with a scalar-field source, proposing a systematic method to extract exact and approximate $F(T)$ solutions by solving conservation laws under power-law and exponential scalar-field ansatzes. By deriving a master equation that ties the torsion function $F(T)$ to the scalar potential and the coframe components, the authors generate extensive families of solutions, including many special cases with closed analytic forms and several with novel special functions. The results illuminate how scalar-field dynamics (quintessence, phantom, and quintom regimes) can be embedded in teleparallel $F(T)$ gravity and show TRW-like late/early cosmology limits, thereby enriching the toolbox for dark-energy modeling in anisotropic cosmologies. The work provides a versatile framework that can be extended to other scalar sources and informs future phenomenological studies of dark energy within teleparallel gravity.

Abstract

In this paper, we investigate time-dependent Kantowski--Sachs spherically symmetric teleparallel $F(T)$ 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, $V\left(φ\right)$, solutions. Then, we find new non-trivial teleparallel $F(T)$ 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 $F(T)$ 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 $F(T)$ solutions for several types of cases. Some new $F(T)$ 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.