On Continued Gravitational Contraction
A heavy star, its fuel spent, collapses without end — and seals itself behind a horizon.
Make a star heavy enough, then take away the fire that holds it up, and gravity does something almost unbelievable: it never stops.
The big idea
A star is a centuries-long balancing act — the inward crush of its own gravity held off by the outward push of heat from nuclear fusion in its core. When the fuel runs out the heat fades and the push dies. A light star settles into a small, dense ember. But Oppenheimer and Snyder asked about a heavy one, where gravity is too strong for anything to resist, and used Einstein's theory of gravity to work out what happens when a star simply falls in on itself without end.
Their answer split in two, depending on who is watching. Ride down with the star and you reach the centre in a flash — a matter of a day or so. Watch from far away and you see the opposite: the star shrinks toward a special size, its ‘gravitational radius’, and then seems to freeze there, its light stretching redder and dimmer until it winks out. The star has sealed itself off from the rest of the universe. What is left is what we now call a black hole.
How it came about
In the 1930s physicists had learned that dead stars do not always rest easy. Subrahmanyan Chandrasekhar showed that a white dwarf heavier than about 1.4 times the Sun would buckle; Oppenheimer and George Volkoff showed that even a ball of neutrons had a ceiling. Robert Oppenheimer — a decade before he led the atomic-bomb laboratory at Los Alamos — turned with his student Hartland Snyder to the obvious next question, and published the answer on 1 September 1939, the very day the Second World War began in Europe. Almost no one took notice. Even Einstein believed such a total collapse could not really happen, and the idea lay nearly forgotten for a quarter of a century.
Why it mattered
This is the paper in which the black hole was born — not as wild speculation but as a straight consequence of Einstein's equations. It introduced one of the strangest ideas in modern physics: a region of space that things can fall into but from which nothing, not even light, can climb back out, ringed by a surface where time itself appears to stop for anyone watching from outside. Every black hole that astronomers now weigh and photograph is a real example of the object these few pages first described.
A way to picture it
Imagine watching a friend swim away down a river that flows faster the farther out they go. At a certain line the current matches their top speed; past it, however hard they stroke back toward you, they cannot gain a metre. To them, crossing that line feels like nothing — they glide straight over. To you on the bank they seem to slow, redden in the fading light, and hang there forever, never quite reaching it. The river is space itself falling inward; the line is the horizon. Drag the clock in the tool below and watch the same collapse from the bank — slowing, reddening, and finally going dark.
Where it sits
Newton's gravity could never have predicted this; it took Einstein's 1915 picture of gravity as curved spacetime — and Karl Schwarzschild's 1916 solution of his equations (also in this Library) — to make a horizon possible at all. Oppenheimer and Snyder showed that a real star could actually build one. The thread runs on through the 1960s renaissance of relativity to LIGO's 2016 recording of two black holes colliding and the first photograph of a black hole's shadow in 2019.
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.
[Part 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. [Part 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.
the star thus tends to close itself off from any communication with a distant observer; only its gravitational field persists.