Perfect fluid kantowski-sachs and bianchi type-III spacetimes and their concircular Symmetry in <i>f(T)</i> theory of gravity

Abstract The aim of this research is to classify Kantowski-Sachs (KS) and Bianchi type-III spacetimes through concircular vector fields in f ( T ) gravity theory. In order to achieve our goal we first obtained field equations for KS and Bianchi type-III spacetimes with perfect fluid as source in f ( T ) theory of gravity and then obtained the concircular symmetry equations. All these equations are solved simultaneously to obtain the vector field components. The whole process enabled us to obtain particular form of the metric functions and conformal factors. It has been found that perfect fluid KS and Bianchi type-III spacetimes allow concircular vector fields of 4-, 5-, 6-, 7- and 15-dimensions in f ( T ) gravity theory. The torsion scalar T , fluid pressure and energy density are all computed in each case. It has been shown that in all cases except one case pressure and density are constants. It has been observed that pressure and density are linked as p = − ρ in all the cases except two case, indicating that these spacetime metrics may represent a vacuum universe or a universe with dark energy. In one case p = ρ , means that the spacetime has an ordinary matter and in other case the pressure of the fluid and density are functions of the cosmic time t . By choosing particular values of the constants in this case, an equation of state p = − ρ can be achieved.