In fact, nothing can stop the collapse. In theory, the matter should quite literally become infinite in density. Infinity is a troublesome concept: how can infinite density be present in a finite universe? The answer is obvious: in some respects, the matter no longer remains in the universe at all.
When gravitational forces have got to this point, we have what is known as a "singularity"; a point at which normal laws simply do not apply.
Actually, things are worse than that. Not only don't normal laws apply, but the relativity equations suggest that no laws apply. Strange things happen in the region of a singularity. Time is reversed. Conservation laws don't work. Causality is a joke: if you could get into the region of a singularity, you really could go back in time and assassinate your grandfather.
In fact, anything could happen, and science ceases to exist; and you don't even have to physically go to the singularity for this to take place. All you have to do is be able to observe one directly, and science has just gone down the drain. That bothers a lot of theorists and scientists, and rather disturbs me as well.
If there is a naked singularity—that is, a singularity not covered with an event horizon—then, at least in potential, there is no order to the universe.
Out of that thing might come ghosties and ghoulies and things that go bump in the night.
What, then, may we do to save science? Why, invoke censorship, of course.
The kind of censorship invoked is called rather whimsically the "Law of Cosmic Censorship," which states that "There shall be no such thing as a naked singularity." All singularities must be decently clothed with an event horizon.
Given cosmic censorship, a number of interesting laws about black holes may be proved: that they never get smaller, that if one is rotating it can't be sped up until the escape velocity is smaller than the speed of light, and a number of other rules that are collectively known as the laws of black hole dynamics.
Unfortunately, cosmic censorship deprives science fiction writers of some of their best stories.
It does it this way. If all black holes are covered with event horizons, it follows that you can't plunge into a black hole and come out elsewhere or elsewhen. Actually, if you plunge into a random black hole, all that could ever come out anywhere would be a stream of undifferentiated sub-nuclear particles; for all their fantastic properties, singularities do retain one feature, namely that gravitation in their region is rather high, sufficient to disassociate not only the molecular, but the atomic, structure of anything visiting them.
On the other hand, if a star about to collapse into black hole status is rotating fast enough, some solutions to the Einstein tensor suggest that the singularity formed will be a donut; you could dive through that and come out in one piece, provided the donut were large enough.
Large enough means galactic sized, I'm afraid; stellar size black holes will still get you too close to the singularity so that you can't use them for transportation. Furthermore, what you come out to on the other side is not, according to the equations, our universe at all. What it will be like, no one can say, except that it will have in it a copy of the black hole you dove through to get there.
So, turn around and dive back, of course; but that doesn't work. You go through and out again, all right, but into a third universe different from either of the other two. The black hole is still there, so try again—and come out in a fourth, and there behind you is that rather tiresome black hole again.
Is any of this real, or are we playing with ideas? No one really knows, of course. The most we can say is that the people who can solve Einstein tensors come up with that kind of result.
It's rather discouraging for science fiction writers. Here we thought we had a new way to get faster than light travel, what with black holes connecting us to another universe, or, just possibly, to another region of our own, and the very people who gave us the black holes go on to prove we can't use them.
Still, maybe there's a way out. Perhaps someone will find a solution. But they can't so long as the law of cosmic censorship is enforced, because singularities decently covered with event horizons can't come out and affect our universe.
* * *
Back to Weber and gravitation waves. One of the models constructed to account for the enormous gravitational energy generated in the center of the galaxy had a very large singularity lurking down there. Suns fell into it, and as they were eaten, gravity waves poured out. It was a rather depressing picture, our galaxy being eaten alive like that.
Then a number of other laboratories constructed gravitational antennae. Bell Laboratories, an English group, the Russians, all made gravity wave detectors. In each case their equipment was supposed to be an improvement on Weber's.
None of them found any coincidences at all. People began to wonder just what Weber had done, and to doubt his results.
Last summer, at a Cambridge Conference of experimental relativists, the picture changed again.
The people who had built "improved" gravity wave antennae reported no results whatever.
Weber continued to report results, but with a change I'll get back to in a moment.
And two other groups, one at Frascati, Italy, the other at Munich, Germany, had built carbon copies of Weber's antenna. They got coincidences. Whatever Weber was observing, others have independently observed something similar now.
Meanwhile, Weber did a re-analysis of his coincidences, using a computer rather than human judgment to define just what was a coincidence. The result was startling. He still gets events—but they are no longer concentrated in the galactic plane. The sidereal coincidences have gone away, and with them has gone the evidence for the large singularity eating the galaxy.
Moreover, Dr. Robert Forward, of Hughes Research at Malibu, California, has constructed his own gravity wave antenna. Since lasers were invented at Hughes Labs, it's no surprise that Forward's antenna employs them. He has three big weights at the apexes of a right-angle triangle.
Lasers measure the precise distance of each weight from the others. A gravity wave will presumably distort that triangle, and thus be detected.
Forward has "events" too. They seem to coincide with the kinds of things Weber gets, but no serious attempt to compare results has been made as I write this.
For that matter, the Munich people have just got started. They were quite surprised, by the way, they'd thought Weber's results were some kind of artifact.
* * *
It appears, then, that some kind of gravity waves do travel about through the universe; at least something that can affect large aluminum cylinders hundreds of kilometers apart is operating here.
The next step is to see if these events have any relationship to the bursts of x-ray energy detected by Vela satellites. At the moment that's not possible, and of course there are a lot more gravity wave events than x-ray events; but if the x-ray events are accompanied by coincidences on the gravity antenna, we'll know a lot more about both.
We may then be able to decide what gravity is: a force, or a distortion of geometry. We may be able to learn more about black holes, and what happens inside them, and who knows, those trips to alternate universes could be a real possibility.
Until we get rid of cosmic censorship, though, we'll never know what happens to the volunteers who go exploring down black holes.
Fuzzy Black Holes Have No Hair
Black Holes have no hair, but they're fuzzy. Because they're fuzzy, they're not really black.
If that seems confusing, read on: it doesn't get a lot clearer, but don't worry about it; not many people in all this world understand, and those that do have to believe three impossible things before breakfast.
In the previous chapter I told you that if a chunk of matter gets squeezed small enough it becomes a black hole. That's about 3 kilometers radius for our Sun. We also gave the equation for the radius for those who know how to punch the buttons on a good scientific calculator.
Actually we don't know the radius of a b
lack hole. What we calculate is the radius of the "Schwarzschild region": that more-or-less sphere within which the surface gravity is so large that light cannot get out, and from which no signals can ever escape. In fact, nothing can escape from within the Schwarzschild radius. Also, down in there somewhere lurks a singularity that does strange things to time and causality.
* * *
If you watched a star collapse you'd never see it get quite so small as that. Instead it would appear that the collapse had slowed down and everything was now hovering just outside the Schwarzschild radius. The light would get redder and redder, and also dimmer and dimmer, and in milliseconds it would go out.
Since nothing can come out of the hole, we can't see in. We call the region from which nothing can escape the "event horizon," and we'll never know what happens inside because of the law of cosmic censorship, which was described in the last chapter.
Classical black hole theory dictates several laws of black hole dynamics. Some aren't too interesting, but the Second Law says the area of the event horizon can never decrease, and increases as matter and energy are pumped into the hole. This means that black holes never get smaller. Feed them matter and/or energy and they grow.
That lets us deduce one thing instantly. What happens if a normal matter and an anti-matter black hole collide? Well, nothing that wouldn't happen if two normal matter holes, or two anti-matter holes, collided, of course. The holes eat each other to form one larger than either, but we'll never know which ones contain normal or anti-matter. In fact, the question is meaningless.
You see, black holes have no hair.
This is a convenient way to say that everything we'll ever know about a black hole can be deduced from three parameters. Once you specify the mass M, the angular momentum J, and the electric charge Q, you've said it all. Nothing remains but location, which isn't important for the physics of the hole, but may be for the physicist who wants to study it.
Mass we understand. It doesn't really matter whether that mass is in the form of energy or matter; Einstein's E=mc2 takes care of that, and down in the hole it's irrelevant whether the rest mass is e or m.
Angular momentum comes from rotation of the object before it collapsed. Naturally it's conserved, so that if the star were rotating, the thing inside the hole rotates as well. It also rotates fast, just as a skater speeds up in a spin when she pulls her arms in.
The last parameter, charge, is just what it says, and it gives us a way to move a black hole around. If it isn't charged, feed it charged particles until it is, then use magnets to tow it.
The laws of black hole dynamics say you can never recover the rest mass energy (that's the Me2 energy, of course) of the original body. It's lost forever. Even shoving anti-matter down the hole gains you nothing.
However, you can get energy out of a spinning black hole. Up to 29% of the rotational energy is available, and in the case of a star that's a lot. To get it you throw something down the hole, and one of the things that comes out is gravity waves.
In our experience gravity waves are puny things, but we're a long way from their source. Up close is another matter entirely. You could be torn apart by them, as the characters in my story, "He Fell Into a Dark Hole," very nearly were.
Most of what we know about black holes comes from Stephen Hawking of the University of Cambridge. Many physicists think Hawking is to Einstein what Einstein was to Newton, and he's still a young man. This year Hawking has added quantum mechanics to classical black hole theory, and he's ruined a lot of good science fiction stories.
* * *
Somewhat over a year ago Larry Niven and I went out to Hughes Research Laboratories in Malibu. As stated previously the laser was invented at Hughes, so they do a lot of laser research there. They're also among the top people in ion drive engines, and they've done a lot with advanced communications concepts.
All that was fascinating, but we went to talk with Dr. Robert Forward, who's one of the experts on gravitation, I'd met him because he liked my black hole story ("He Fell Into a Dark Hole," nominated for a Hugo, but alas . . .)
Bob Forward is the inventor of the Forward Mass Detector, a widget that can track a tank miles away by mass alone. (It can't distinguish between a tank at a mile and a fly on the end of the instrument, but if you use two and triangulate you're safe enough.) His detector can also be lowered into oil wells, or towed behind an airplane to map mass concentrations below.
After lunch we talked about black holes. Dr. Forward was particularly interested in Stephen Hawking's then new notion that tiny black holes might have been formed during the Big Bang of Creation. Since the Second Law predicts that they never get smaller, there should be holes of all sizes left. Some might be in our solar system.
They would come to rest in the interior of large masses. There might be quite a large one inside the Sun, for example, and even in the Earth and Moon as well. A very large mass hole, say 108 kilograms, would still be very small: about 10-19 centimeters radius. An atomic radius is around 10-9 cm., very large compared to such a hole, so that the hole couldn't eat many atoms a day, and wouldn't grow fast.
Black holes inside the Earth or Sun aren't too useful because they're hard to get at. Bob Forward wanted to go to the asteroids. You search for a rock that weighs far too much for its size. Push the rock aside and there in the orbit where the asteroid used to be you'll find a little black hole.
You could do a lot with such a hole. For example, you could wiggle it with magnetic fields to produce gravity waves at precise frequencies. There might be all sizes of holes, even down to a kilogram or two.
It sounded marvelous. Larry and I figured there were a dozen stories there. I'd already written my black hole story, and Larry hadn't, so he beat me into print with a thing called "The Hole Man." All I got from the trip was a couple articles and columns.
Well, Larry's story (which won a Hugo. Sigh.) has just been reprinted in his new collection, while the columns I did about little black holes have been forgotten—I hope!
I'm glad I have nothing in print about tiny black holes, because Hawking has just proved they can't exist. Oh, they can be formed all right, but they won't be around very long. It seems that black holes aren't really black. They radiate, and left to themselves they get smaller all the time. The Second Law needs modifying.
Hawking points out that Einstein's general relativity, which produces most of the primary equations for black holes, is a classical theory. It doesn't take quantum effects into account.
Hawking corrects this. In quantum theory a length, L, is not fixed. It has an uncertainty or fluctuation on the order of Lo/L, where Lo is the Planck length 10-33 cm.
Since there is uncertainty in the length scale, it follows that the event horizon of the black hole isn't actually fixed. It fluctuates through the uncertainty region.
In fact, the black hole is FUZZY, and energy and radiation can tunnel out of the hole to escape forever. It's the same kind of effect as observed in tunnel diodes, where particles appear on the other side of a potential barrier.
Since black holes have no hair, although they do have fuzz, the quantum radiation temperature—that is, the rate at which they radiate—must depend entirely on mass, angular momentum, and charge.
It does, but I'm not going to prove it for you. Hawking uses math that I can tool up to follow, but I'm not really keen on Hermetian scalar fields, and I doubt many readers are either. If you want his proof, send a dollar to Gravity Research Foundation, 58 Middle Street, Gloucester, Mass. 01930 and request a copy of Hawking's paper "Black Holes Aren't Black."
Hawking shows that the temperature of a black hole is,
T=1026M
where M is mass in grams, and T is degrees Kelvin, and the lifetime of a black hole in seconds is
tL=10-26 M3
Using my new Texas Instruments SR-50 that handles scientific notation and takes powers and roots in milliseconds, it wasn't hard to work up Figure 11 from these equations.*
There
are more numbers than we need, of course. It's a consequence of the pocket computer. Not long ago I'd have had to use logs and slide rule, and I'd have done no more than I needed. Now look.
The first thing to see is that small holes have uninteresting lifetimes. In order for one to be around long enough to use it, the hole must be massive.
Any black holes formed in the Big Bang would be 1010 years old now; so if they weren't larger than a small asteroid they're gone already. Worse, that exponential decay rate defeats us even if we find a hole just decayed to an interesting size. It will still vanish too fast to use.
So there went Larry's "Hole Man", and two stories I had plotted but hadn't written, and I suspect a lot of other science fiction as well. Sometimes I feel a bit like Alice when she protested, "Things flow here so!"
A Step Farther Out Page 15
