Conformal symmetry classes for pp-wave spacetimes

TL;DR

This paper classifies conformal symmetries in pp-wave spacetimes, refining previous isometry classifications, and identifies the maximum number of proper conformal Killing vectors, providing a detailed symmetry analysis.

Contribution

It refines the classification of conformal symmetries in pp-wave spacetimes and establishes new results on the maximum number of proper conformal Killing vectors.

Findings

Maximum of three proper non-special conformal Killing vectors in type N pp-waves.

Every conformal Killing vector in null fluid type N pp-waves is a conformal Ricci collineation.

New isometry classes of pp-wave spacetimes are identified.

Abstract

We determine conformal symmetry classes for the pp-wave spacetimes. This refines the isometry classification scheme given by Sippel and Goenner (1986 {\it Gen. Rel. Grav.} {\bf 18} 1229). It is shown that every conformal Killing vector for the null fluid type $N$ pp-wave spacetimes is a conformal Ricci collineation. The maximum number of proper non-special conformal Killing vectors in a type $N$ pp-wave spacetime is shown to be three, and we determine the form of a particular set of type $N$ pp-wave spacetimes admitting such conformal Killing vectors. We determine the conformal symmetries of each type $N$ isometry class of Sippel and Goenner and present new isometry classes.