A simple test for spacetime symmetry

TL;DR

This paper introduces a straightforward method leveraging curvature conditions from Killing equations to analyze spacetime symmetries, including Killing vectors and tensors, applied to various metrics like Kerr in four and five dimensions.

Contribution

The paper presents a novel, simple approach to investigate spacetime symmetries using curvature conditions, enabling bounds on symmetries and aiding in solving Killing equations.

Findings

Applied method to Kerr metric revealing its Killing-Yano symmetries.

Derived upper bounds on the number of Killing vectors and tensors.

Extended analysis to various four- and five-dimensional metrics.

Abstract

This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to compute an upper bound on the number of Killing vector fields, as well as Killing-Yano tensors and closed conformal Killing-Yano tensors. We also use them in the integration of the Killing equations. By means of the method, we thoroughly investigate Killing-Yano symmetry of type D vacuum solutions such as the Kerr metric in four dimensions. The method is also applied to a large variety of physical metrics in four and five dimensions.