Ricci Soliton Vector Fields of a Sub-Class of Perfect Fluid Bianchi Type-I Spacetimes in f(T) Theory of Gravity

This paper investigates the Ricci solitons of a sub-class of Bianchi type-I spacetimes in f(T) theory of gravity in the presence of perfect fluid. It is found that special sub-classes of perfect fluid Bianchi type-I metrics admit steady, shrinking and expanding Ricci solitons. To tackle the problem, RS equations are explored along with their integrability conditions. Field equations in f(T) theory are derived for the spacetime metric. By solving the field equations we derived general form for f(T). Ricci soliton equations and field equations are solved simultaneously to explore the corresponding Ricci soliton vector fields. We found Ricci soliton vector fields of dimension 4, 5, 6, 7, 8, 10 and 11. In some cases the corresponding metrics are Einstein metrics while in other cases non-Einstein metrics are also obtained which admit Ricci soliton vector fields. The physical quantities \(\rho \), p, T and f(T) related to each solution are also calculated. Another interesting aspect of our results is that we obtained some non-linear f(T) functions for which field equations possess solutions and those solutions admit Ricci soliton vector fields.