editorial by John W. Campbell

There have been a number of articles on the "black hole" phenomenon in a variety of scientific magazines—from the most erudite super-mathematical discussions to the most general popular explanations. As might be expected in dealing with such way-out speculative material, each of the various articles has covered the concepts from a slightly different aspect, considered slightly different consequences, and thus came up with slightly different stories.

In the true sense, each of those discussions in the high-power specialized journals of physics, cosmology and astronomy has been a science-fiction story—each has sought to extrapolate from known data, and currently accepted general theory, what the consequences of extreme conditions would be. Such stories as Hal Clement's "Mission of Gravity" and "Close to Critical" were precisely that sort of science fiction— massive speculation, with a minimum of actual knowledge.

If you haven't yet read one of the articles on the "black hole" phenomenon, the essence is this:

Given a massive star five or more times as massive as Sol, it will consume its nuclear fuel at a much faster rate than Sol. All of its hydrogen will be fused to helium, and the star will then begin to condense under gravitational forces, while the central, core temperature goes up into the range of hundreds of millions of degrees. Under these conditions of temperature and pressure, helium itself can be fused to successively heavier elements:

2 He⁴ à Be⁸ + He⁴ à C¹² + He⁴ à O¹⁶ + He⁴ à Ne²⁰ . . . This series of additions of He⁴ permits the remaining nuclear energy of the "ashes" of hydrogen fusion reactions to be consumed, until the build-up reaches iron. Iron represents the lowest point on the "packing fraction curve"—which expresses the amount of energy per nucleon the nucleus contains, and, therefore, the stability of that nucleus. The nuclei in the region of Fe⁵⁶ are right at the bottom of the curve; hydrogen, of course, has the highest energy—that's why it releases so much energy when the protons are combined to helium.

Atoms with nuclei more complex than iron tend to release energy when they come apart—Prime Example No. One being, of course, uranium. Uranium yields energy not by combining to make more complex nuclei, but by fissioning to produce simpler ones.

So our spendthrift star reaches a point where all available nuclear energy has been extracted from its matter—but that force physicists call the "weak" force of gravity, begins to really take over.

A normal star is like an airplane; it's able to defy gravity by a constant application of power. If a plane's engine quits, if it runs out of fuel, it can continue to fly for a while by gliding, by using gravitational energy to keep it moving.

There is, however, a very definite, crunching end to that. Gravitational energy has a tendency to wind up by converting all the remaining energy into light, heat, mechanical distortion, and noise.

Precisely that happens in a star; when it can no longer provide energy output sufficient to "keep flying," to hold its outer layers out by radiation pressure, it falls inward.

When it does that, it appears to be a positive feedback mechanism—and like all positive feedback mechanisms, it goes to completion in an incredible hurry. Once the inner collapse of the star's core starts, the increased density resulting from the partial collapse increases the gravitational intensity, which tends to increase the tendency to collapse. The increased gravitational force causes increased inward acceleration. Which causes greater density faster, which multiplies the collapse-force, which speeds the ...

Estimates of the time-for-collapse of the stellar core when this sort of thing starts vary; there seems to be general agreement that the maximum time required for the collapse of the core of a giant star—several times more massive than our Sun—may be as long as one hundred seconds. Other analyses indicate it may take only slightly longer than the time required for a light-speed pulse to cross the diameter of the stellar core, say one to two seconds.

In any case, immediately after the collapse, there is a neutron star about a dozen miles in diameter where there used to be a 100,000 to 200,000 mile diameter stellar core. And in that instant after the collapse, the temperature of that core material has been driven up to billions of degrees by the release of the stupendous gravitational energy—and there's a fantastic pulse of radiant energy driving outward.

That pulse of energy is violent enough to blast some 80-90% of the star's original mass out into deep space. The explosion is so violent-beyond-concepts-of-violence that all the heavy elements much beyond iron are formed during the first few minutes as the outer layers are heated beyond thermonuclear temperatures.

For the next few days, the collapsed star will be throwing off energy faster than the combined total of the energy output of all the other stars in its galaxy. A dozen galaxies away, astronomers will notice a new supernova has bloomed.

In chemistry there's a basic principle that reactions tend to go in the direction which lessens the energy-stress in the system. Thus one volume of nitrogen plus three volumes of hydrogen can combine to form only two volumes of ammonia; the Haber process puts hydrogen and nitrogen under high pressure, which encourages the formation of the desired product since doing so relieves the pressure.

The energy density and violence in an exploding supernova's atmosphere is such that uranium and the transuranic elements form in immense quantities—it represents a reversal of the uranium-fission reaction, and by absorbing the energy of fission, lessens slightly the violence of the supernova environment. In effect, a supernova causes a uranium bomb to implode.

Since no human being can truly appreciate the appalling violence of a fission explosion, the supernova explosion is unimaginably-squared, so to speak.

At the center of this violence, collapsing at the center of the detonation, is the stellar core—which undergoes a number of interesting changes.

Angular momentum is conserved; since the original star was rotating, this collapsed remnant is rotating—but the rate has changed because of the drastic shortening of its radius of gyration. A figure skater builds up spin speed by starting her spin with arms extended, then bringing them in close to her axis of spin, the collapsing stellar core does somewhat the same on an exaggerated scale. The spin-rate increases from the once-a-day-or-so rate of an ordinary star of its class—the Class B and A giants rotate much more rapidly than do the F, G and later classes such as the Sun—to something on the order of 300 to 1,000 times per second.

It is now a neutron star, and a pulsar.

The stupendous temperature to which the core material was heated during the collapse produced a variety of effects, to which the now stupendous gravitational force adds some refinements. The surface gravity of something twice as massive as our Sun, with a diameter of 12-15 miles is measured in multimillions of G's. Our best structural materials, under such a gravity, would flow into monomolecular films—assuming they were somehow miraculously protected from the hundreds of millions of degrees of heat.

But strange things happen to matter under the conditions of a neutron star; it isn't made up entirely of neutrons—for various complex reasons, there are still lots of protons mixed in with the neutrons, so that the material is a superconductor. (We're having trouble getting room-temperature superconductors; neutron stars are superconductors at some 10⁸ or 10⁹ degrees.) Also, near the surface of the neutron star, the outermost layers crystallize into a solid crust. This is no ordinary solid, naturally; it's hotter than the core of a star like the Sun, yet a crystalline solid. It has a tensile strength and stiffness you can remember as being around a hundred million million million times that of steel, in the neighborhood of 10²⁹ times.

Because it had a magnetic field when the star collapsed, and became superconductive, the neutron star is a superconductive magnet—the magnetic field couldn't escape from the superconductive material. But the magnetic field was imploded by the collapse along with the matter it was tied to; the magnetic field of a neutron star is probably the strongest, densest tightest magnetic field in the Universe.

That magnetic field tends to add stiffness to the already fantastic stiffness of the crust of the star.

No process as vast and violent as a supernova explosion can be perfectly symmetrical, homogeneous or smooth; the resultant neutron star is spinning, but normally the magnetic field doesn't wind up trapped exactly along the axis of rotation of the star. And the magnetic field will not be exactly uniform, like a lecture-room diagram. And the distribution of mass won't be exactly uniform .

And the neutron star is not quite the end of the line; there is still further evolution to be undergone.

For one thing, that magnetic field reaches out for millions of miles, and keeps stirring up the still-cooling gases of the outer mantle of the original star. It generates light and radio energies in the process, and accelerates the ions of those gases to cosmic-ray relativistic velocities. While no electromagnetic structure cap exceed the speed of light, a beam of magnetic force reaching out from a spinning star must, at some distance, be sweeping at 99.9999999 +% the speed of light, and be accelerating ions to very relativistic speeds.

But this work and momentum must necessarily be derived at the expense of the spinning neutron star. The ions of the outer gases are accelerated, and the neutron star is gradually slowed in doing so.

Even with the horrendous surface gravity of a neutron star, if some thing fifteen miles in diameter is spinning at three hundred times a second, it will not be a perfect sphere; it's going to be an oblate spheroid, with an equatorial bulge.

When it slows its spin somewhat, the shape of the star will readjust, of course—and it's going to do it despite the super-super-super straitjacket of that crust 10²⁹ times as strong as steel! Not even that super-solid crystalline material can stand up to the sort of gravity forces at the surface of a neutron star.

The fascinating thing is that the results of such neutron "star-quakes" have been observed by astronomers! Not as structural changes seen by telescopes, of course—but because when there is a star-quake, and a resultant redistribution of mass—on a very minute and gentle scale, that's what happened to Los Angeles last spring; the San Gabriel mountains rose some four feet—there's a change in the distribution of angular momentum, and consequently a change in the rate of spin of the star. Since neutron star pulsars send out their pulses with exceedingly high precision, any minute change in the rate of spin can be detected and measured.

A star-quake in which the crust yields as little as one thousandth of a centimeter is readily detectable; that crystalline crust stuff has an appallingly high density remember, and it's out at the outermost periphery of the star. Just a minute shift represents movement of a mass equal to half a dozen Earths, perhaps. (And the energy released, if you put it on a hypothetical extension of the Richter scale, would probably be something like 100. The Richter scale goes only to 10—because much greater energy than that released here on Earth wouldn't leave anybody around to talk about it.)

So . . . we have the neutron stars, which we detect as pulsars. And we have evidence that old pulsars have much lower rates of spin. That is, pulsars are still evolving—that isn't a stable end to the evolution of a giant star.

It's also known that some stars are not merely five or ten times as massive as the Sun—some of them appear to be sixty to eighty times as massive. Such stars are, of course, immensely luminous; they burn their nuclear fuel as much as 100,000 times as fast as Sol, and they're strictly dedicated to a short life but a merry one. The probable lifetime of such a star is well under 500,000 years.

All calculations indicate that when it finally goes into collapse—it can't stop at the neutron-star stage. The implosion of the burnt-out core, when it comes, will be so violent, the temperatures so extreme, and the inward pressures of gravity plus the implosion effect between infalling core and the outward-blasting over-layers such that the core material will be driven beyond the neutron-star stage.

All the protons will be crushed out of existence—and even the neutrons begin to lose identity. And things happen to the resultant gravitational field.

Compressed beyond even the maximum density of nuclear matter, beyond even the density of neutrons themselves, the gravitational forces do weird things.

The surface gravity becomes so high that the escape velocity required for a particle to escape the gravity field may rise to, say, 200,000 miles per second. I.e., if you wanted to fire a particle from the surface of the collapsar, so that it could drive out against its immense gravitational field and escape into space, it would have to be launched with a velocity of 200,000 miles per second.

Since a photon is energy, and therefore mass, and cannot travel faster than 186,000 miles per second—not even a quantum of radiant energy could escape such a surface!

Of course, if you were already in orbit around such a collapsar, and didn't have to fight your way out from the surface itself, you could get free with less velocity. That is, there is a zone at some distance from the collapsar itself at which you could establish an orbit with an orbital speed of a mere 186,000 miles a second.

Anything venturing inside that zone would be absolutely trapped. Nothing whatever can come out from within that zone; the collapsar exists at the bottom of a gravitational well so deep that nothing can escape once it gets in there.

This zone is, of course, extremely esoteric; the things happening at that level in the gravity well can only be expressed in relativistic terms—and as one major scientist said, it amounts to a genuine science-fiction space-time warp! Relativity involves recognition that space dimensions and time have a true metrical relationship; at that strange surface, known for the man who first explored it mathematically as a Schwartzchild Discontinuity, the time dimension tends to replace one of the space dimensions in an exceedingly complex way. A ship that tried to reach the collapsar could not exceed the speed of light—yet it would be accelerated under a stupendous gravity force all the way in. Oddly, with a finite distance to go, it would, theoretically, take a near-infinite time to reach the star! The time-expansion effects would be exceedingly complex!

If a man somehow got his spaceship inside the Schwartzchild Discontinuity around a collapsar, he could never report back as to what he saw, and, of course, could never return. And he wouldn't get very far, anyway, due to tidal effects.

On Earth if you go ten feet up, there is a minute change in the gravitational force acting on you. Grayitometers have beenmade which are sufficiently sensitive to measure such a difference in the acceleration of gravity due to a ten-foot difference in elevation. Since gravitational force varies with the inverse square of the distance, you're heavier on the ground than on the upper floors of a building—even if it does take super laboratory instruments to detect it!

The gravity field around a collapsar is something else again. At any given level, say a mile from the surface, the absolute value of the field is appalling—hundreds or thousands of millions of Gs. And the value will have dropped to a quarter of that stupendous value if you go another mile or so; the rate of decline is even more fantastic than the value itself.

But it's the difference between gravitational acceleration at one end of an object, and the acceleration value at the farther end that produces tidal forces.

The tidal forces around a collapsar are of such magnitude that the nuclei of atoms will be disrupted by tidal forces.

If you lowered a rod through a Schwartzchild Discontinuity into a collapsar's field, not only would it be impossible to pull it out—no information can travel outward through a Schwartzchild Discontinuity—but the outer end of the rod would be stretched apart and broken mechanically by the tidal forces, while the inner end of the rod's matter was undergoing nuclear dissolution.

Since no information can escape from a Schwartzchild Discontinuity, it is impossible to see one, detect it by radar, X rays or any other probing technique. Not even its magnetic field can escape!

It is totally cut off from the Universe—save in one respect. That gravitational field that is the operating agency of collapsars will still be present and to be accounted for!

Naturally, since we now have an invisible black ghost to consider—the Black Hole Star—a lot of long-time puzzles of astronomy and astrophysics are up for review in the non-light of this new possibility.

One puzzle that's cropped up repeatedly is the mystery of the star Epsilon Aurigae B.

Epsilon Aurigae is a binary; the A, or brighter star, is a supergiant FO-type of very high luminosity 60,000 times our sun—it's a massive (and, therefore, brilliant and short-lived) star with a companion. They make an eclipsing pair—i.e., the 27 year binary orbit plane is such that Earth happens to be almost exactly in that plane, and we see A and B pass in front of each other.

The light-curve of the eclipse is, however, most peculiar. When the B star eclipses its brilliant companion, the decline of light-level indicates we're seeing A through star B—that B is mostly transparent.

Which might be acceptable if it weren't that the orbits indicate that star B is itself enormously massive, many times more massive than our Sun.

Assorted explanations have been tried; some years back it made head lines as the largest star known because they tried explaining that light curve on the basis that the B star was a super-super-super-swollen Red Giant type about two billion miles in diameter, and of such low temperature we practically didn't see it at all against the glare of its huge, brilliant companion.

More recently that's gone out of acceptance for assorted reasons based on further data; for a while it was explained as a more ordinary massive star, with a vast tail of matter that was being exuded along its orbital path. Sort of a diamond ring effect—a ring of gas-dust with' the "jewel" being the B star itself.

One trouble was that no one's caught the spectrum of the B star itself well enough to be able to say anything about its nature.

So, naturally—they're now considering that the B star is a collapsar, a black hole, while the queer eclipse pattern is caused by some of the debris of the supernova explosion that produced the collapsar. The debris of gas and dust remains trapped by the gravitational fields of the A and B stars—but naturally, you can't see the B star itself—you couldn't if you were right there in orbit around the pair.

Of course the A star managed to survive the catastrophic demise of its companion—but it won't for long. Stars that big and brilliant have short life spans; presently it, too, will detonate and collapse into a Schwartz-child Discontinuity, leaving nothing but some gas-dust debris orbiting behind two black holes, a practically totally invisible black ghost binary.

The cosmologists like this idea for their own reasons; current theories are in trouble because the curvature of space derived from astronomical measurements does not match what their theories maintain it should be for the quantity of mass observed. There should be many times more mass than has ever been detected to produce the observed characteristics of space.

Black holes could account for the missing mass—it's here all right, but unobservable.

And it does not all have to be in such weird systems as two black holes orbiting each other; there's an entirely different type of black hole that does not involve such extreme conditions as the collapsar. That is the Black Galaxy—the entire galaxy that constitutes a Schwartzchild Discontinuity, but does not have to involve collapsar conditions.

The essence of the black hole effect is that nothing can escape its gravitational field—that even a quantum of light will be dragged back by the gravitational field, because the escape velocity exceeds 186,000 miles per second. The collapsar achieves that effect by fantastic density resulting in a stupendous surface gravity—by immense concentration of gravitational force.

Now you can stop a bullet with a quarter inch of exceedingly strong, dense, and hard armor plate—but you can stop it just as thoroughly with a bale of cotton, too. The cotton is neither hard, dense, nor exceedingly strong—but it clings and enwraps and slows the bullet. It doesn't even distort the bullet—but it stops it just as completely as the armor plate could.

The gravitational field of a galaxy isn't very intense of course—but it extends out and out over distances you don't measure in miles, but in kilo-parsecs. It's not violently intense, but it persists over vast distances, light-year after light-year taking its toll of anything seeking to escape.

It can be shown mathematically that a dense galaxy—and that means a quite livable density, not star-touching-star type of thing, less dens,: actually than some of the known star clusters!—may have a gravitational field so strong and so extensive that no ray of light, no radio wave, not even an X or cosmic ray, can ever leave it—nor could any spaceship subject to the normal laws of relativity. Assuming a continuing operation of a drive mechanism capable of developing thrust greater than the force of the galactic gravity, it would appear that such a ship could, at least theoretically, climb out of that Schwartzchild black hole. Sorry—no dice. The total amount of energy required is necessarily greater than E = mc² allows. Even if 100% of the mass of the ship were converted to driving energy, it wouldn't be sufficient to climb out of the gravitational well.

A Black Galaxy would achieve, by the long, long slope of a gravitational field reaching out megaparsecs what a collapsar's field achieves by immense concentration of force.

Both would be absolutely inescapable.

But the Black Galaxy would be a weird place to visit! Just what would happen to a ship falling into such a Black Galaxy calls for some really fancy analysis! Coming in from outside, it would not encounter the vicious tidal forces that can disrupt nuclei, because the Black Galaxy field isn't anywhere intense just extensive. But since the escape velocity of the field exceeds the speed of light, anything coming into that field would be accelerated to . . . well, what speed? Could it be accelerated in, at parabolic or hyperbolic velocity, and shoot out the other side, having acquired energy of fall sufficient to achieve an escape, even though that escape requires faster-than-light speed? If not, what happens to the excess energy?

Of course inside the Black Galaxy could be stars with planets and intelligent races who observed the starry heavens around them. What would they see of the universe outside? What happens to radiation falling into a gravity field with that greater-than-c escape velocity?

Once in a while the serious cosmologists come up with concepts and ideas that no science-fictioneer has been bold enough to dream up!

The Editor.