Which 1939 model describes collapse of a uniform dust sphere into a black hole?

The Oppenheimer–Snyder model describes the gravitational collapse of a uniform, pressureless dust sphere into a black hole. Robert Oppenheimer and Hartland Snyder published the model in 1939, making it one of the earliest relativistic calculations of stellar collapse leading to black-hole formation.

To keep Einstein’s equations tractable, they assumed a perfectly spherical, nonrotating body with uniform density, zero pressure, no radiation, and no mass ejection. Inside the collapsing sphere, the matter follows a simple homogeneous cosmological solution; outside it, spacetime is described by the Schwarzschild solution. In the idealized model, the surface crosses its Schwarzschild radius and an event horizon forms before the central singularity.

Real stars are far more complicated: they rotate, have pressure gradients, lose mass, radiate, and may fragment or produce shocks. The model is therefore not a detailed stellar forecast. Its importance is conceptual and mathematical: it showed clearly that general relativity permits continued collapse beyond the point at which a black hole forms.