On Axially Symmetric Space-Times Admitting Homothetic Vector Fields in Lyra's Geometry

TL;DR

This paper explores axially symmetric space-times within Lyra's geometry, classifying solutions to Einstein's field equations that admit homothetic vector fields, considering cases where the displacement vector varies with time or remains constant.

Contribution

It provides a classification of homothetic solutions in Lyra's geometry for axially symmetric space-times, a novel analysis in this geometric framework.

Findings

Classification of solutions with time-dependent displacement vector

Classification of solutions with constant displacement vector

Explicit solutions exhibiting homothetic symmetry 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 (EFE) for the space-time under consideration, which display a homothetic symmetry.