2026/05/13 by Christine C. Dantas
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1142/s0218271826410142
Honorable Mention in the Gravity Research Foundation 2026 Awards for Essays on Gravitation. A new section was included, with new references. A few other minor improvements were also made; 16 pages. Accepted for publication in the International Journal of Modern Physics D
arxiv created 2026/07/22 · arxiv updated 2026/08/03
The Eisenhart-Duval lift (ED) geometrizes classical dynamics by embedding their trajectories into null geodesics of a higher-dimensional Lorentzian spacetime. However, such a construction requires a natural Hamiltonian, that is, quadratic in the canonical momenta. As a consequence, mini-superspace cosmological models governed by non-natural Hamiltonians cannot admit an ED lift. Effective models in Loop Quantum Cosmology provide a concrete example: polymer-modified Hamiltonians become non-polynomial in the momenta and therefore fall outside the metric framework of the ED lift. We thus establish a kinematical no-go theorem: non-quadratic cosmological dynamics cannot be geometrized via ED constructions. Quantum-corrected bounce models therefore illustrate a structural limitation of metric geometrization within the ED framework. A few qualitative comments on the possibility of Stäckel-lifting a single-degree-of-freedom non-natural Hamiltonian in quantum cosmology is also presented.