On Axially Symmetric Space-Times Admitting Homothetic Vector Fields in   Lyra's Geometry
  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 (EFE) for the space-time under consideration, which display a homothetic symmetry. 
Ragab M. Gad and A. E. Al Mazrooei
gr-qc