On September 1, 1939, the same day Germany invaded Poland, J. Robert Oppenheimer and his student Hartland Snyder published a five-page paper that would help lay the mathematical foundations of black-hole physics.

Their paper, “,” published in Physical Review, used Einstein’s general theory of relativity to show how a sufficiently massive star could collapse under its own gravity, contracting beyond its gravitational radius and becoming inaccessible to distant observers.

It was a remarkable theoretical result. Yet its arrival coincided with the outbreak of World War II, and the discovery attracted little immediate attention.

Oppenheimer would soon turn his attention to nuclear physics and the wartime effort that would eventually lead him to direct the Los Alamos laboratory. He never published another paper in astrophysics.

One of his most remarkable theoretical contributions was eclipsed by the very war that would ultimately define his career.

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When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star’s mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected.