What happens when gravitational waves punch through a collapsing universe?

Working with a toroidal universe under T2 symmetry, the authors prove that Einstein's equations remain well-defined even when curvature collapses into Dirac-mass spikes — the gravitational equivalent of a sonic boom. They establish the first non-perturbative global theory at this low regularity, proving stability for well-behaved initial data and genuine instability for oscillatory data, where the geometry forces unexpected corrections to the energy content of matter. The result matters because it extends rigorous mathematical control over spacetime evolution into territory previously considered too singular to handle.