Potentials and point symmetries of Klein–Gordon equations in space-time homogenous Gödel-type metrics

Abstract

In this paper, we study the geometric properties of generators for the Klein–Gordon equation on classes of space-time homogeneous Gödel-type metrics. Our analysis complements the study involving the “Symmetries of geodesic motion in Gödel-type spacetimes” by U. Camci (J. Cosmol. Astropart. Phys., doi: 10.1088/1475-7516/2014/07/002 ). These symmetries or Killing vectors (KVs) are used to construct potential functions admitted by the Klein–Gordon equation. The criteria for the potential function originates from three primary sources, viz. through generators that are identically the Killing algebra, or with the KV fields that are recast into linear combinations and third, real subalgebras within the Killing algebra. This leads to a classification of the [Formula: see text] Klein–Gordon equation according to the catalogue of infinitesimal Lie and Noether point symmetries admitted. A comprehensive list of group invariant functions is provided and their application to analytic solutions is discussed.