Ricci-flat spacetimes admitting higher rank Killing tensors

Abstract

Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which admit irreducible Killing tensors of rank-3 or rank-4. The construction relies upon the Eisenhart lift applied to Drach's two-dimensional integrable systems which is followed by the oxidation with respect to free parameters. In four dimensions, some of our solutions are anti-self-dual.

arXiv comment12 pages

References in corpus (12)

• Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Kleinian Geometry and the N=2 Superstring
• Remarks on l-conformal extension of the Newton-Hooke algebra
• On the Drach superintegrable systems
• Some Spacetimes with Higher Rank Killing-Stackel Tensors
• Generalised Eisenhart lift of the Toda chain
• Killing tensors and canonical geometry
• Higher rank Killing tensors and Calogero model
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Twistor geometry of a pair of second order ODEs
• Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors

Cited by in corpus (12)

• Black holes, hidden symmetries, and complete integrability
• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Eisenhart lift for higher derivative systems
• Null lifts and projective dynamics
• Eisenhart lift of Koopman-von Neumann mechanics
• Self-dual metrics with maximally superintegrable geodesic flows
• Eisenhart Lift of $2$--Dimensional Mechanics
• Slowly rotating black holes with exact Killing tensor symmetries
• Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter
• Some metrics admitting nonpolynomial first integrals of the geodesic equation
• More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
• The Bohlin variant of the Eisenhart lift