When does collapsing matter first form a cosmic traffic jam?

Cosmic structure forms when matter streams cross and pile up — a moment called the catastrophe time. Starting from Burgers-type fluid dynamics in a spherical gravitational field, the authors derive a perturbative expression for this crossing time in Newtonian gravity and show it is governed by a single dimensionless ratio involving mass, initial radius, and initial velocity gradient — not local gravitational acceleration alone. This means the expansion stays accurate even where gravity is strong. They then extend the result to radial geodesic motion in Schwarzschild spacetime, connecting Zel'dovich-style approximations to general relativity.