Killing tensors in pp-wave spacetimes

TL;DR

This paper provides a comprehensive solution to the second order Killing tensor equations in pp-wave spacetimes, revealing the maximum number of irreducible Killing tensors and their relation to spacetime symmetries.

Contribution

It fully solves the Killing tensor equations for specific pp-wave spacetimes, including conformally flat plane waves, and characterizes the conditions for irreducible Killing tensors.

Findings

Maximum of six independent irreducible Killing tensors in conformally flat plane waves

Every pp-wave with an homothety admits a Koutras type Killing tensor

Most such Killing tensors are irreducible except in singular scale-invariant cases

Abstract

The formal solution of the second order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.