On axially symmetric space-times admitting homothetic vector fields in Lyra's geometry

Abstract

This paper investigates axially symmetric space-times that admit a homothetic vector field based on Lyra's geometry. The cases when the displacement vector is a function of t and when it is constant are studied. In the context of this geometry, we find and classify the solutions of the Einstein's field equations for the space-time under consideration, which display a homothetic symmetry.