In classical dynamics, Eisenhart lift connects the dynamics of null geodesics in a Brinkmann spacetime with a continuous family of Hamiltonian systems by means of a suitable projection. In this work we explore the possibility of building a model for quantum dynamics of massless particles propagating inside a Brinkmann spacetime from the Einsenhart lift. As a result, we describe spatial tunneling between regions classically disconnected for a certain class of null geodesics because of curvature. Also we describe entangled states arising from observers who have limited access to the whole Brinkmann space. Finally we explore the possibility of finding a quantum field theory behind these quantum phenomena.

• Received 5 August 2023
• Accepted 15 September 2023

DOI:https://doi.org/10.1103/PhysRevD.108.086006