Closed conformal Killing-Yano tensor and geodesic integrability

TL;DR

This paper demonstrates that the presence of a specific closed conformal Killing-Yano tensor guarantees the existence of mutually commuting Killing tensors and vectors, facilitating the separation of variables in geodesic equations.

Contribution

It establishes a link between a single closed conformal Killing-Yano tensor and integrability conditions for geodesic equations, providing new insights into spacetime symmetries.

Findings

Existence of mutually commuting Killing tensors and vectors

Conditions for separation of variables in Hamilton-Jacobi equations

Implications for spacetime symmetry and integrability

Abstract

Assuming the existence of a single rank-2 closed conformal Killing-Yano tensor with a certain symmetry we show that there exist mutually commuting rank-2 Killing tensors and Killing vectors. We also discuss the condition of separation of variables for the geodesic Hamilton-Jacobi equations.