Noether gauge symmetry classes for pp-wave spacetimes

TL;DR

This paper classifies Noether gauge symmetries in pp-wave spacetimes, revealing the maximum symmetries and deriving new exact solutions of geodesic equations based on these symmetries.

Contribution

It systematically determines Noether gauge symmetry classes for pp-wave spacetimes and finds new exact solutions of geodesic equations using these symmetries.

Findings

Type N pp-wave admits up to 8 Noether gauge symmetries

Conformally flat plane waves have 10 symmetries

New exact geodesic solutions are derived in specific symmetry classes

Abstract

The Noether gauge symmetries of geodesic Lagrangian for the pp-wave spacetimes are determined in each of the Noether gauge symmetry classes of the pp-wave spacetimes. It is shown that a type N pp-wave spacetime can admit at most three Noether gauge symmetry, and furthermore the number of Noether gauge symmetries turn out to be four, five, six, seven and eight. We found that all conformally flat plane wave spacetimes admit the maximal, i.e. ten, Noether gauge symmetry. Also it is found that if the pp-wave spacetime is non-conformally flat plane wave, then the number of Noether gauge symmetry is nine or ten. By means of the obtained Noether constants the search of the exact solutions of the geodesic equations for the pp-wave spacetimes is considered and we found new exact solutions of the geodesic equations in some special Noether gauge symmetry classes.