Introduces a proof of the Lorentzian splitting theorems in general relativity that replaces the linear d'Alembertian (wave operator) with a nonlinear, negative-homogeneity p-d'Alembert operator whose convex Hamiltonian makes it nonuniformly elliptic on future-directed functions. Because ellipticity restores a strong maximum principle and a Bochner-type identity, the classical Riemannian Cheeger-Gromoll Busemann-function argument transfers to spacetimes, yielding a simplified proof that a strong-energy-condition spacetime containing a timelike line splits isometrically as a metric product of a line with a Ricci-nonnegative factor. The core idea is to trade linearity for ellipticity, opening a route toward nonsmooth, low-regularity metrics for a synthetic theory of gravity.
A graduate lecture (McCann, Forward from the Fields Medal 2024 Proceedings) on extending the Riemannian splitting theorems to Lorentzian signature toward a nonsmooth theory of gravity. Its central de…