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.
Roger Penrose (whom we will meet again in a later chronicle) pointed out in 1969 that it is possible for a particle to dive in towards a Kerr black hole, split in two when it is inside the ergosphere, and then have part of it ejected in such a way that it has more total energy than the whole particle that went in. If this is done, we have extracted energy from the black hole.
Where has that energy come from? Black holes may be mysterious, but we still do not expect that energy can be created from nothing.
Note that we said a Kerr black hole — not a Schwarzschild black hole. The energy we extract comes from the rotational energy of the spinning black hole, and if a hole is not spinning, no energy can possibly be extracted from it in this way. As McAndrew remarked, a Schwarzschild hole is dull, a dead object that cannot be used to provide power. A Kerr black hole, on the other hand, is one of the most efficient energy sources imaginable, better by far than most nuclear fission or fusion processes. (A Kerr-Newman black hole allows the same energy extraction process, but we have to be a little more careful, since only part of the ergosphere can be used.)
If a Kerr-Newman black hole starts out with only a little spin energy, the energy-extraction process can be worked in reverse, to provide more rotational energy — the process that McAndrew referred to as “spin-up” of the kernel. “Spin-down” is the opposite process, the one that extracts energy. A brief paper by Christodoulou in the Physical Review Letters of 1970 discussed the limits on this process, and pointed out that you could only spin-up a kernel to a certain limit, termed an “extreme” Kerr solution. Past that limit (which can never be achieved using the Penrose process) a solution can be written to the Einstein field equations. This was done by Tomimatsu and Sato, and presented in 1972 in another one-page paper in Physical Review Letters. It is a very odd solution indeed. It has no event horizon, which means that activities there are not shielded from the rest of the Universe as they are for the usual kernels. And it has what is referred to as a “naked singularity” associated with it, where cause and effect relationships no longer apply. This bizarre object was discussed by Gibbons and Russell-Clark, in 1973, in yet another paper in Physical Review Letters.
That seems to leave us in pretty good shape. Everything so far has been completely consistent with current physics. We have kernels that can be spun up and spun down by well-defined procedures — and if we allow that McAndrew could somehow take a kernel past the extreme form, we would indeed have something with a naked singularity. It seems improbable that such a physical situation could exist, but if it did, space-time there would be highly peculiar. The existence of certain space-time symmetry directions — called killing vectors — that we find for all usual Kerr-Newman black holes would not be guaranteed. Everything is fine.