Self-dual metrics with maximally superintegrable geodesic flows
arXiv:1504.03826 · doi:10.1103/PhysRevD.91.104020
Abstract
A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-Euclidean spacetime of signature (1,1). It is characterized by the presence of a second rank Killing tensor. Spacetimes of the ultrahyperbolic signature (2,q) with q > 2, which admit a second rank Killing tensor and possess superintegrable geodesic flows, are built.
V2: 11 pages, minor modifications