The situation finally changed in 1939. In that year, Oppenheimer and Snyder were studying the collapse of a star under gravitational forces — a situation which certainly did have physical significance, since it is a common stellar occurrence.
Two remarks made in their summary are worth quoting directly: “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 the sun, this contraction will continue indefinitely.” In other words, not only can a star collapse, but if it is heavy enough there is no way that the collapse and contraction can be stopped. And “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.” This is the first modern picture of a black hole, a body with a gravitational field so strong that light cannot escape from it. (We have to say “modern picture” because before 1800 it had been noted as a curiosity that a sufficiently massive body could have an escape velocity from its surface that exceeded the speed of light; in a sense, the black hole was predicted more than two hundred years ago.)
Notice that the collapsing body does not have to contract indefinitely if it is the size of the Sun or smaller, so we do not have to worry that the Earth, say, or the Moon, will shrink indefinitely to become a black hole. Notice also that there is a reference to the “gravitational radius” of the black hole. This was something that came straight out of the Schwarzschild solution, the distance where the reddening of light became infinite, so that any light coming from inside that radius could never be seen by an outside observer. Since the gravitational radius for the Sun is only about three kilometers, if the Sun were squeezed down to this size conditions inside the collapsed body defy the imagination. The density of matter must be about twenty billion tons per cubic centimeter.
You might think that Oppenheimer and Snyder’s paper, with its apparently bizarre conclusions, would have produced a sensation. In fact, it aroused little notice for a long time. It too was looked at as a mathematical oddity, a result that physicists needn’t take too seriously.
What was going on here? The Schwarzschild solution had been left on the shelf for a generation, and now the Oppenheimer results were in their turn regarded with no more than mild interest.
One could argue that in the 1920s the attention of leading physicists was elsewhere, as they tried to drink from the fire-hose flood of theory and experiment that established quantum theory. But what about the 1940s and 1950s? Why didn’t whole groups of physicists explore the consequences for general relativity and astrophysics of an indefinitely collapsing stellar mass?
Various explanations could be offered, but I favor one that can be stated in a single word: Einstein. He was a gigantic figure, stretching out over everything in physics for the first half of this century. Even now, he casts an enormous shadow over the whole field. Until his death in 1955, researchers in general relativity and gravitation felt a constant awareness of his presence, of his genius peering over their shoulder. If Einstein had not been able to penetrate the mystery, went the unspoken argument, what chance do the rest of us have? Not until after his death was there a resurgence of interest and spectacular progress in general relativity. And it was one of the leaders of that resurgence, John Wheeler, who in 1958 provided the inspired name for the Schwarzschild solution needed to capture everyone’s fancy: the black hole.
We still have not reached the kernel. The black hole that Wheeler named was still the Schwarzschild black hole, the object that McAndrew spoke of with such derision. It had a mass, and possibly an electric charge, but that was all. The next development came in 1963, and it was a big surprise to everyone working in the field.
Roy Kerr, at that time associated with the University of Texas at Austin, had been exploring a particular set of Einstein’s field equations that assumed an unusually simple form for the metric (the metric is the thing that defines distances in a curved space-time). The analysis was highly mathematical and seemed wholly abstract, until Kerr found that he could produce a form of exact solution to the equations. The solution included the Schwarzschild solution as a special case, but there was more; it provided in addition another quantity that Kerr was able to associate with spin.
In the Physical Review Letters of September, 1963, Kerr published a one-page paper with the not-too-catchy title, “Gravitational field of a spinning mass as an example of algebraically special metrics.” In this paper he described the Kerr solution for a spinning black hole. I think it is fair to say that everyone, probably including Kerr himself, was astonished.
The Kerr black hole has a number of fascinating properties, but before we get to them let us take the one final step needed to reach the kernel. In 1965 Ezra Newman and colleagues at the University of Pittsburgh published a short note in the Journal of Mathematical Physics, pointing out that the Kerr solution could be generated from the Schwarzschild solution by a curious mathematical trick, in which a real coordinate was replaced by a complex one. They also realized that the same trick could be applied to the charged black hole, and thus they were able to provide a solution for a rotating, charged black hole: the Kerr-Newman black hole, that I call the kernel.
The kernel has all the nice features admired by McAndrew. Because it is charged, you can move it about using electric and magnetic fields. Because you can add and withdraw rotational energy, you can use it as a power source and a power reservoir. A Schwarzschild black hole lacks these desirable qualities. As McAndrew says, it just sits there.
One might think that this is just the beginning. There could be black holes that have mass, charge, spin, axial asymmetry, dipole moments, quadrupole moments, and many other properties. It turns out that this is not the case. The only properties that a black hole can possess are mass, charge, spin and magnetic moment — and the last one is uniquely fixed by the other three.
This strange result, often stated as the theorem “A black hole has no hair” (i.e. no detailed structure) was established to most people’s satisfaction in a powerful series of papers in 1967-1972 by Werner Israel, Brandon Carter, and Stephen Hawking. A black hole is fixed uniquely by its mass, spin, and electric charge. Kernels are the end of the line, and they represent the most general kind of black hole that physics permits.
After 1965, more people were working on general relativity and gravitation, and other properties of the Kerr-Newman black holes rapidly followed. Some of them were very strange. For example, the Schwarzschild black hole has a characteristic surface associated with it, a sphere where the reddening of light becomes infinite, and from within which no information can ever be sent to the outside world. This surface has various names: the surface of infinite red shift, the trapping surface, the one-way membrane, and the event horizon. But the Kerr-Newman black holes turn out to have two characteristic surfaces associated with them, and the surface of infinite red shift is in this case distinct from the event horizon.
To visualize these surfaces, take a hamburger bun and hollow out the inside enough to let you put a round hamburger patty entirely within it. For a Kerr-Newman black hole, the outer surface of the bread (which is a sort of ellipsoid in shape) is the surface of infinite red shift, the “static limit” within which no particle can remain at rest, no matter how hard its rocket engines work. Inside the bun, the surface of the meat patty is a sphere, the “event horizon,” from which no light or particle can ever escape. We can never find out anything about what goes on within the meat patty’s surface, so its composition must be a complete mystery (you may have eaten hamburgers that left the same impression). For a rotating black hole, these bun and patty surfaces touch only at the north and south poles of the axis of rotation (the top and bottom centers of the bun). The really interesting region, however, is that between these two surfaces — the remaining bread, usually called the ergosphere. It has a property which allows the kernel to become a power kernel.