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.

27 pages, no figures, v2: minor changes and references added, version to appear in Class. Quant. Grav

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• Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution
• Wormhole $C$ metric
• $\mathcal{I}$-degenerate pseudo-Riemannian metrics
• Discrete scale invariance in holography revisited
• Counting the number of Killing vectors in a 3D spacetime
• Euclidean supersymmetric solutions with the self-dual Weyl tensor
• Conserved quantities and integrability for massless spinning particles in general relativity
• Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring
• Integrability Conditions for Killing-Yano Tensors and Maximally Symmetric Spaces in the Presence of Torsion
• Antisymmetric tensor generalizations of affine vector fields
• Closed conformal Killing-Yano initial data