Some metrics admitting nonpolynomial first integrals of the geodesic equation

Abstract

It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are constructed, each of which revealing a chain of generalised Killing vectors.

V2: 14 pages, minor improvements, the version to appear in PLB

References in corpus (4)

• Ricci-flat spacetimes admitting higher rank Killing tensors
• Eisenhart lift for higher derivative systems
• Self-dual metrics with maximally superintegrable geodesic flows
• Eisenhart Lift of $2$--Dimensional Mechanics