Higher rank Killing tensors and Calogero model

TL;DR

This paper constructs a higher-dimensional Lorentzian spacetime with irreducible Killing tensors of high rank by applying the Eisenhart lift to the Calogero model, revealing new geometric structures.

Contribution

It introduces a novel geometric construction linking the Calogero model to higher-rank Killing tensors via Eisenhart lift.

Findings

Construction of (n+2)-dimensional spacetime with high-rank Killing tensors

Establishment of a geometric link between Calogero model and spacetime symmetries

Identification of irreducible Killing tensors of rank up to n

Abstract

(n+2)-dimensional Lorentzian spacetime which admits irreducible Killing tensors of rank up to n is constructed by applying the Eisenhart lift to the Calogero model.