Noether gauge symmetry classes for pp-wave spacetimes

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 nonconformally 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.

Physical Significance of Noether Symmetries

“…These symmetries have also been obtained for some of the Bianchi-type spacetimes in [49][50][51][52]. The complete analysis of Noether symmetries for Gödel-type and pp-wave spacetimes studied by Camci et al [53][54][55].…”

Integration of the geodesic equations via Noether symmetries

“…where prime ( ′ ) denotes derivative with respect to the radial coordinate r. All STH Riemannian manifolds endowed with the Gödel-type spacetime (10) are obtained by solving equations in (11) as follows:…”

pp-waves in modified gravity

“…The Killing symmetries of the pp-wave metrics have studied by Sippel and Goenner, and by Bondi et al [26,27] for variety of profile functions in both pseudo-Riemannian and Riemann-Cartan geometry settings (see, also Chapter 23 [14]). Noether gauge symmetries of the pp-wave metric have recently been discussed in [28].…”