Killing-Yano symmetry for a class of spacetimes admitting parallel null 1-planes

TL;DR

This paper explores a generalized class of spacetimes with parallel null 1-planes, identifying Killing-Yano tensors and their associated Killing tensors, and examines the relationship between geometric duality and symmetries.

Contribution

It introduces a broader class of metrics extending gpp-waves, finds their Killing-Yano tensors, and analyzes the compatibility of duality with non-generic symmetries.

Findings

Killing-Yano tensors of order two and three are explicitly constructed.

The zero-curvature condition for the generalized metrics is established.

Compatibility between geometric duality and non-generic symmetries is demonstrated.

Abstract

A possible generalization of plane fronted waves with parallel rays (gpp-wave) fall into a more general class of metrics admitting parallel null 1-planes. For gpp-wave metric, the zero-curvature condition is given, the Killing-Yano tensors of order two and three are found and the corresponding Killing tensors are constructed. Henceforth, the compatibility between geometric duality and non-generic symmetries is presented.