Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes

摘要

Highlights • A complete classification of the Lie and Noether point symmetries for the Klein–Gordon and for the wave equation in pp-wave spacetimes is obtained. • The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes. • The functional form of the potential is determined in which the Klein–Gordon equation admits point symmetries and Noetherian conservation law. Further the point and Noether symmetries of the wave equation are derived. Abstract A complete classification of the Lie and Noether point symmetries for the Klein–Gordon and the wave equation in pp-wave spacetimes is obtained. The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes. Employing the existing results for the isometry classes of the pp-wave spacetimes, the functional form of the potential is determined for which the Klein–Gordon equation admits point symmetries and Noetherian conservation law. Finally the Lie and Noether point symmetries of the wave equation are derived.