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.

12 pages

References in corpus (3)

• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Remarks on l-conformal extension of the Newton-Hooke algebra
• Conformal Killing Tensors and covariant Hamiltonian Dynamics

Cited by in corpus (8)

• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Eisenhart lift for higher derivative systems
• Eisenhart lift of Koopman-von Neumann mechanics
• Self-dual metrics with maximally superintegrable geodesic flows
• Eisenhart Lift of $2$--Dimensional Mechanics
• Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter
• Some metrics admitting nonpolynomial first integrals of the geodesic equation
• The Bohlin variant of the Eisenhart lift