Nonnoetherian Lorentzian manifolds

A nonnoetherian spacetime is a Lorentzian manifold that contains a set of causal curves with no distinct interior points, called 'pointal curves'. This new geometry recently arose in the study of nonnoetherian coordinate rings in algebraic geometry. We investigate properties of metrics on nonnoetherian spacetimes, and use the Hodge star operator to show that free dust particles have spin $\tfrac 12$. We also reproduce the Kochen-Specker $\psi$-epistemic model of spin using the nonnoetherian metric, and show similarities between our model and spin entanglement for Bell states and four-photon entanglement swapping. Finally, we determine the stress-energy tensor of dust on such spacetimes, and find that it is only nonzero at points where dust is created or annihilated.
Comment: 25 pages