Eisenhart lift for higher derivative systems

Understand

The Eisenhart lift provides an elegant geometric description of a dynamical system of second order in terms of null geodesics of the Brinkmann-type metric.

• In this work, we attempt to generalize the Eisenhart method so as to encompass higher derivative models.
• The analysis relies upon Ostrogradsky's Hamiltonian.
• A consistent geometric description seems feasible only for a particular class of potentials.