Dual Metrics for a Class of Radiative Spacetimes

TL;DR

This paper investigates the properties of dual spacetimes with parallel null one-planes, focusing on Killing tensors and radiation conditions to understand their physical significance and invariance.

Contribution

It introduces conditions under which dual spacetimes preserve physical properties, linking Killing tensors with radiation conditions in specific spacetime subclasses.

Findings

Identifies conditions for dual spacetimes to retain physical properties

Analyzes the role of Killing tensors in radiative spacetimes

Provides a framework for understanding duality in spacetime metrics

Abstract

Second rank non-degenerate Killing tensors for some subclasses of spacetimes admitting parallel null one-planes are investigated. Lichn\'erowicz radiation conditions are imposed to provide a physical meaning to spacetimes whose metrics are described through their associated second rank Killing tensors. Conditions under which the dual spacetimes retain the same physical properties are presented.