A study of energy conditions in Kantowski-Sachs spacetimes via homothetic vector fields

In this paper, we have studied different energy conditions for some metrics arising from the classification of Kantowski-Sachs spacetimes via homothetic vector fields (HVFs). The homothetic equations for Kantowski-Sachs spacetimes are analyzed using a Maple algorithm which transforms these equations to the reduced involutive form (Rif), giving all possible cases in the form of a tree, known as Rif tree, where the branches of the resulting tree give the potential spacetime metrics which may possess proper HVFs. The set of homothetic equations is integrated for all branches of the Rif tree and the explicit form of HVFs is obtained in ease case. For all the obtained metrics, we have found the bounds for different energy conditions. The stability of these metrics is also discussed.