A simple test for spacetime symmetry

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.