The intriguing questions of cosmology are: How did it all start? How will it all end?
   Cosmologists have spent centuries studying, theorizing, and arguing about origins—the origin of the Earth, the solar system, the stars and galaxies, the universe. In the past few years, though, the discoveries of the quasars and pulsars, neutron stars and exploding galaxies, have forced them to look into the question of endings.
   In particular, the phenomenon of gravitational collapse has come under careful study. It turns out to be a weird and wonderful domain wherein might lie the secret energy source of the quasars, the power behind galactic explosions, a domain where massive stars can wink out and completely leave this universe, and—just maybe—a domain in which we might find the answer to faster-than-light travel.
   Like so much of the past decade's new astronomical thinking, it was the quasars that prompted an intense look at the mechanics of gravitational collapse. The energy output of the quasars is so huge that old ideas about energy production in stars and galaxies had to make way for new concepts. As Table I shows, a typical quasar is emitting more visible light energy than a thousand Milky Way galaxies! And as much radio energy as the strongest radio sources known.
   
   
   
   Just to put those very large numbers in some sort of context: M 87 is one of the largest and brightest (optically) galaxies. It probably contains a trillion (1012) stars. Yet the quasars are typically a hundred times brighter. Cygnus A is one of the strongest radio sources in the sky, and the quasars are just as powerful in radio output. The energy output for quasars shown in Table I is roughly equal to the energy emitted in ten billion supernova explosions, or the energy obtained by the total annihilation of ten million stars.
   Could there be ten billion supernovas blazing in chain reaction in a quasar? Or 107 solar masses of matter and antimatter merrily destroying each other in a million-year-long celestial fireworks?
   And although the quasars seem to be emitting as much, or more energy, as the most powerful optical and radio sources in the heavens, they are apparently much smaller than any galaxy. How can the energy of a thousand galaxies be packed into a space that's considerably smaller than a single galaxy?
   
   So far, we've tacitly assumed that the quasars are "cosmologically" distant—a billion light-years or more away from us. This put them out at the edges of the observable universe, for the most part. This is exactly what astronomers did in the early 1960s, when they first realized that the quasars are very different from anything they had previously seen. 
   
   
   
Fig. 1. The observed red shifts of several quasars and the galaxy 3C 295, believed to be the farthest-known true galaxy. The curve shows how the red shift is related to the object's recession speed, based on the assumption that the red shifts are due to the expansion of the universe. Curiously, no quasar has been observed to show a red shift much beyond the 80% of lightspeed mark.
Note: The drawings shown here are taken from IN QUEST OF QUASARS, by Ben Bova, and are reprinted with permission of Crowell-Collier Publishing Co.
   
   The reason that the quasars were assumed to be "cosmologically" distant is that they show tremendous red shifts. The farthest known true galaxy, 3C 296, has a red shift that's estimated to represent a speed of recession of 36% of the speed of light. This works out to a very rough distance estimate of five billion lightyears. Most quasars do much better. A handful of quasars have such huge red shifts that they're apparently moving at 80% of lightspeed; this yields a distance judgment of 10 billion light-years. Curiously, 80% of c seems to be the limit of the quasars' recession speed; none have been observed going any faster.
   
   
   
Fig. 2. The Hubble relationship of red shift to distance for a group of distant galaxies. No quasars are shown on this graph. The trend of the data for galaxies favors the Big Bang cosmology; that is, the farthest galaxies tend to be brighter and more numerous _than would be predicted by the Steady State cosmology. If the quasars are truly at cosmological distances (5 to 10 billion lightyears) they would lend still more weight to the Big Bang theory.
   
   This red shift method for gauging cosmic distances is, at best, very rough, and depends on an interlinking chain of assumptions: (1)that the observed red shifts are Doppler shifts, caused by the objects' rushing away from us; (2) that the reason they're moving away is that the whole universe is expanding, and expanding uniformly, so that the farther away a galaxy or quasar is from us the faster it's receding; therefore; (3) the larger the red shift, the faster the object is receding, and thus the greater its distance from us.
   This whole red shift business started with the American astronomer Edwin P. Hubble, who announced in 1929 that all the farther galaxies—outside our own Local Group of 17 gravity-linked galaxies—show red shifts. Moreover, Hubble showed that if you make a graph plotting the brightnesses of galaxies against their red shifts, the relationship is a beautiful straight line. This is extremely powerful evidence that the red shifts are truly related to distance.
   But, if you plot the brightnesses of the known quasars against their red shifts, you don't get a straight line at all. You get a wild shotgun pattern, with no apparent relationship to anything except confusion.
   This led Fred Hoyle, the British cosmologist, to begin wondering if the quasars' red shifts might be completely unrelated to distance. Maybe the quasars are not cosmologically distant at all, but relatively nearby, perhaps only a few million light-years away, at most.
   Recognize that Hoyle needed "local" quasars if he was to save his well-known Steady State theory of cosmology. For the quasars—if cosmologically distant—tended to show that the universe was definitely very different 10 billion years ago than it is today. If you count the quasars and galaxies together, the universe was more densely packed with such objects 10 billion years ago than it is now. All this destroys the Steady State theory, which claims that the universe has always been about the same as it is now.
   
   The opposing Big Bang cosmology pictures the origin of the universe in one cataclysmic burst of energy. Many cosmologists looked on the quasars as evidence for that primal explosion. But, if Hoyle could show that the quasars are local objects, and not related to events of 10 billion years ago, then the Steady State theory might still survive. On the other hand, if it could be shown that the quasars are local and their red shifts not related to distance, then some doubt gets cast on the value of red shift measurements for judging the distances of all the galaxies. Some doubt might even be cast on the very concept of an expanding universe. So the local vs. cosmological quasar argument had—and still has—high stakes attached to it.
   Thus it was in 1963 that Hoyle and William Fowler, astrophysicist from CalTech, proposed that the quasars might be supermassive objects relatively close to our own galaxy. They saw the quasars as being much smaller than a galaxy, perhaps like a globular star cluster, but with a mass of 100 million times the sun's. For lack of a better tag, call it a superstar.
   Both the energy output and the red shift of the Hoyle-Fowler superstar was attributed to gravity. Gravitational collapse provided the basic energy for the superstar's outpouring of light and radio waves, as gravitational energy is converted to electromagnetic while the superstar shrinks in size and becomes constantly denser, more compact. And the powerful gravitational field of this supermassive object causes the red shift. As photons work "uphill" against such a strong gravitational field, they are shifted down toward the red end of the spectrum. Similar effects, although much smaller in magnitude, have been observed on the sun and other stars.
   The superstar idea came under immediate attack—as have all theories hoping to explain the quasars. A single object of 108 solar- masses could not remain stable, said the physicists. All right, said the theory's backers, call it a super-star-cluster, then. It can still be treated as a single object even if it consists of many smaller parts. And, they showed, if the superstar were rotating rapidly enough, it would not break up.
   The argument is still going on. Big Bang cosmologists want the quasars to be cosmologically distant. Steady State people want them local. In all fairness, there have been several other suggestions that the quasars are local. For example, James Terrell of the University of California proposed in 1964 that the quasars might be something like massive star clusters that have been shot out of our own or nearby galaxies. The red shifts, then, would be Dopplershifts caused by the ejected quasars' recession, but would have no relation to cosmology.
   That same year, C. R. Lynds of Lick Observatory and Alan Sandage of CalTech showed definitely that the galaxy M 82 was in the throes of an explosion. Its core had blasted itself apart, perhaps as recently as a few hundred thousand years earlier. Could the quasars be "shrapnel" fired out of exploding galaxies?
   More on galactic explosions shortly.
   The idea of gravitational collapse powering the quasars was not restricted to local-quasar enthusiasts. Even the astronomers and cosmologists who backed the cosmologically-distant quasar theory considered gravitational energy as a possible source of the quasars' enormous brightness. In this case, they looked on the quasar as something about the size of a galaxy that's collapsing inward on itself. The energy release could be purely gravitational in origin, or it could come from the collision and explosion of billions of stars in the galaxy's core, as they were squeezed together in the general collapse of the galaxy.
   
   
Fig. 3. Plots of quasar red shifts vs. optical magnitudes (top) and radio magnitudes (below) show no discernible pattern. The straight-line Hubble relationship of normal galaxies does not apply for quasars, lending some doubt to the conclusion that the quasars are cosmologically distant.
   
   The discovery of the quasars and the earlier realization that the so-called radio galaxies frequently have small regions in their cores from which most of the radio energy emanates, led astronomers to begin paying more attention to what's going on in the cores of galaxies.
   They dusted off the work done in the 1940s by the American astronomer C. K. Seyfert, who studied a number of galaxies that have extraordinarily bright cores. Seyfert galaxies, as they're now called, have very active cores in which there's much loose gas that's highly excited and moving with velocities of some 4,500 km /sec. While Seyfert worked exclusively with optical telescopes—radio astronomy was still only a gleam in Grote Reber's eye—more recent radio studies of the Seyfert galaxies show them to be fairly powerful radio sources, with the radio emission coming from those bright, agitated cores. Incidentally, the Seyfert galaxies resemble the quasars in many respects, including the fact that they both tend to show sizable variations in light and radio output. But the quasars are at least a thousand times more powerful—if they're cosmologically distant.
   By the mid-1960s evidence for galactic explosions began pouring in. Lynds and Sandage showed that M 82 Ls exploding. Short-exposure photographs of M 87 showed that it has an optically bright spot at its core, with a jet of glowing plasma, some 30,000 light-years long, streaking off to one side! Previous photos of M 87, longtime exposures to catch the faintest star clusters around it, had washed out this feature completely.
   There's even a strong chance that our own galaxy suffered a core explosion at least a million years ago. There's a "halo" of radio-emitting gases around the Milky Way that could have been ejected from the core in an explosion similar to M 82's. Some astronomers now believe that most, if not all, of the radio activity in galaxies and quasars is associated with explosions at the core.
   What causes galactic explosions? Where does the energy come from? Is it a coincidence that the energy involved in an exploding galaxy, according to most calculations, works out to be very similar to the energy output from the quasars?
   
   
Fig. 4. An exploding galaxy, M 82. The light areas are the main body of the galaxy, photographed in normal light. The dark region shows vast jets of gas, photographed in the light of ionized hydrogen and printed in negative for contrast. The explosion filaments are roughly 14,000 lightyears long and moving with velocities of about 1000 km/sec.
   
   As in the case of the quasars, theoretical explanations for galactic explosions abound. Again, they include outright gravitational collapse, stellar collisions and /or supernova chain reactions, and matter-antimatter annihilation. Each possibility needs some sort of gravitational collapse to make it work. And again, none of the explanations can answer all the tests and objections that have been brought out.
   As you might suspect, all this attention on gravitational collapse as a power source for quasars and exploding galaxies led the astronomers and cosmologists to turn expectantly to the physicists for some answers. And that's just what they got—some answers. Not the answers they were looking for, alas, but some fascinating food for further thought.
   The physicists had been following the same gravitational-collapse trail from a different starting point. They were studying individual stars in an attempt to explain the evolution of a star—an evolution that sometimes ends in a supernova explosion. It's ironic that the physicists were sniffing along this trail because of their interest in what was, up to the mid-1960s, the most titanic catastrophe known to man: a supernova. And when they bumped noses with the astronomers, it was because the astronomers had found cataclyms ten billion times mightier.
   
   Let's get away from quasars and galaxies for a while, and start thinking about plain little old stars—like the sun. In following the physicists over this portion of the trail, we'll soon enough re-emerge into the wider cosmos of pulsars, neutron stars, quasars, expanding and contracting universes, and—as advertised earlier—maybe faster-than-light travel.
   Stars begin life with gravitational collapse. The sun, for example, was a loose cloud of gas and dust some five billion years ago. Under its own gravitational forces, the cloud contracted in an astronomical eyeblink about 50 million years, according to computer calculations—and formed a medium-sized star and some cosmic debris orbiting around it.
   Why did that gravitational collapse stop where it did, leaving the sun with its present almost perfectly spherical diameter of 1.39 million kilometers? Because at the sun's central temperature of some 20 million degrees Kelvin, hydrogen fusion reactions produce enough gas and radiation pressure to balance the still-present gravitational pull of 2 x 1027 tons of matter.
   In another five to ten billion years, the sun's hydrogen supply will start to run low. Most of its core will be helium, created from the hydrogen fusion process. The core will thus be denser than it is now, and hotter. Its central temperature will rise to some 100 million degrees, and then the helium will begin to fuse into carbon, oxygen and neon.
   At the higher core temperatures associated with this new energy source, gravity must yield somewhat to increased gas and radiation pressure. The sun's outer layers will expand. The surface of the sun—photosphere—will become distended and cooler. The sun will become a red giant star.
   The same routine gets repeated over and again. As the fusion reactions in the sun's core produce constantly heavier elements, the core temperature rises. The higher the core temperature, the easier to start fusion reactions with the heavier elements, leading to the creation of still-heavier elements, still-higher temperatures, and so on.
   Each cycle of new-element-building goes faster than the previous one. Each cycle is bringing the sun closer to disaster. Through it all, gravity is constantly being outfought by rising gas and radiation pressures, and the sun's outer envelope becomes hugely distended. And despite the higher core temperatures, the surface temperature still goes down.
   Until the fusion reactions at the core produce iron. When iron nuclei fuse they produce lighter elements, not heavier ones. The game is over. And gravity, which has been patiently waiting all this time, becomes the victor. The remainder of the star's life will depend more on the always-abiding force of gravity than on any other factor.
   What happens then?
   
   Since 1915, when the first white dwarf star was discovered—the Pup of Sirius—astronomers and astrophysicists have assumed that somehow most stars must eventually end up as dying white dwarfs. But how does a star go from being a red giant to a white dwarf? (It sounds like a question out of a fairy tale, rather than a problem in nuclear astrophysics.)
   And stars have been known to explode. Sometimes rather mildly, in cosmic burps called novas; sometimes dramatically, in supernova explosions that release as much energy in twenty-four hours as the sun emits over a billion years. Where do these stellar explosions fit in? Will the sun explode?
   These are the questions that the astrophysicists were working on when the quasar storm struck. One of the leading workers in this field, who has concentrated his studies on the phenomenon of gravitational collapse, is Kip S. Thorne, an associate professor of theoretical physics at CalTech who's barely out of his twenties. Much of what follows is based on his work ... and the printouts of his computer.
   When a star loses the last of its nuclear fuel, or at least loses so much that gas and radiation pressure can no longer keep the star expanded, the ever-present gravitational force in the star becomes the dominant factor in its fate.
   For stars of the sun's mass, the story appears to be straightforward. Computer analyses tell us that once gas and radiation pressures can no longer support the star's size, gravity begins to compress the star. It falls inward on itself. The interior density and temperature rise as the gravitational collapse progresses, and eventually this produces a braking action.
   The sun's eventual collapse may take place over the span of a few million years. Gradually it will sink from its grossly distended red-giant diameter to a diameter more like our own Earth's—about 12,700 kilometers—and its central temperature will reach nearly a billion degrees. The density at the core will go up to about a thousand tons per cubic inch. The sun will be a white dwarf star.
   
   
   
   
Fig. 5. The elliptical galaxy M 87, one of the largest and brightest galaxies in the heavens, shown here in a long-exposure photograph to capture the faint star clusters orbiting around the galaxy's main body.
   
   Why does the gravitational collapse stop at this point? The star is composed of a plasma, which consists of ions—atomic nuclei that have been stripped of their orbital electrons—and the freed electrons. As the density of the plasma increases, these particles collide more and more frequently. The electrons, which can be thought of as a hazy cloud rather than a firm particle, can undergo some compression. And they do, getting squeezed further and further as the gravitational collapse forces the star's density higher and higher. At a density of about a thousand tons per cubic inch, though, the electrons resist further compression.
   This produces the braking action—the counterforce that finally balances out against gravity and stops any further collapse of the star.
   So now we have a star that's about the size of the Earth, although it still contains just about 2 x 1027 tons of matter.
   During this contraction phase there may have been some unburned fusible material in the sun's outer layers. But as the interior temperature soared, any fusible elements—from hydrogen to iron—would eventually be heated to their ignition temperature and go off like a bomb. Thorne believes that this may explain the pulsars. More on that later.
   
   The final fate of the sun after having reached white dwarfdom seems rather prosaic. It simply cools off, as the heat generated from the collapse is slowly dissipated into space. The process may take billions of years, but eventually the sun will be nothing more than a cold, dark body, the size of the Earth, with a density of some thousand tons per cubic inch.
   But if it's drama you want, consider the fate of the more massive stars.
   The computer calculations show that stars with more than 1.4 times the sun's mass don't stop their gravitational collapse when they reach the white dwarf stage. For stars this massive, the electrons' resistance to compression doesn't give enough of a braking force to counteract the gravitational force. The collapse goes on. There are a number of different possibilities as to what happens next. Much depends on the details of the individual star's mass, spin rate, and chemical composition. But the general outlines of the story appear to be firm.
   If there is enough unburned fusible material in the star's outer shell, the rapidly rising heat of the core may trigger a supernova explosion. As we've already seen, in a supernova the star may release as much as a billion years worth of solar output inside of twenty-four hours. And, although it seems hard to picture anything as surviving such a blast, it now seems certain that the core of the star remains relatively intact, at least for this type of supernova.
   Whether or not there's a supernova explosion, the core of the star keeps on shrinking, past the density of a white dwarf. As the star's diameter keeps getting smaller and its density higher, gravity gets stronger and stronger. If the original star was massive enough, the gravitational force eventually becomes so powerful that the electrons can no longer resist further compression. They are squeezed into the atomic nuclei, turning all the protons in the nuclei into neutrons.
   We now have a mass roughly equal to the sun's consisting entirely of neutrons, some 1057 of 'em, packed side-by-side in a sphere no more than 100 kilometers wide. Probably more like 10 kilometers across. Density is around a billion tons per cubic inch. 
   That's a neutron star.
   
   
   
Fig. 6. The heart of M 87, in a short-exposure photograph that shows the very bright core and the 30,000-lightyear-long plasma jet. Both the core and the jet are strong radio sources.
   
   If the star is not more than two solar masses, the tremendous repulsive forces that the neutrons exert on each other will resist any further gravitational crushing. The brakes are on—neutron brakes this time—and the collapse stops.
   But the story doesn't end there. Far from it!
   The star's core has collapsed to neutron-star dimensions. But there are still outer layers of the star, even if much of this material has been blown off in one or more explosions.
   This outer shell falls in on the tiny neutron core, since gravity is always hard at work. The impact creates enough heat to drive the core's surface temperature up to billions of degrees for a fraction of a second. Under these circumstances most of the heat energy is converted into neutrinos. Not to be confused with neutrons, neutrinos are aloof little particles, much like photons except that under ordinary circumstances a neutrino can penetrate 50 light-years of lead without being stopped.
   But the conditions around a neutron star are far from ordinary. The densities and temperatures of the plasma around the neutron core are so high that even the evasive neutrinos can travel only a few meters before they are deflected, or absorbed. Most of their enormous energy is imparted to the plasma clouds, heating them to tens of billions of degrees. You get a supernova explosion, of course. But this is a different type of supernova—a core supernova that blows away everything except the tiny neutron star core.
   All this—the collapse into the neutron core, the infall of the shell of plasma, the heating that forms neutrinos, the core supernova explosion—all this happens in a few seconds.
   
   The results? Look at the Crab Nebula, that cloud of plasma a few light-years across, still expanding at several hundred kilometers per second more than 900 years after the core supernova that created it, emitting visible light, radio waves, X rays and even gamma radiation.
   And in the center of the Crab Nebula, beautifully verifying the whole theoretical story, is a pulsar!
   For the pulsars, most astronomers firmly believe, are actually neutron stars that are emitting sharply-timed bursts of radio energy.
   The first pulsar, CP 1919—meaning Cambridge Pulsar at 19 hours, 19 minutes right ascension—was discovered during the summer of 1967 by Jocelyn Bell and Anthony Hewish of the Cambridge University radio observatory. CP 1919 is in the constellation Vulpecula, the Fox, a faint and shapeless star-group that lies between the bright stars Vega and Altair. Shortly afterward, a half-dozen additional pulsars were found. More are being detected constantly. The Crab Nebula pulsar is designated NP 0532.
   When the first pulsars were discovered, their precisely-timed radio bursts led some astronomers to wonder if these signals might not be coming from an intelligent civilization in space. For a few weeks they were informally called LGM signals—for Little Green Men.
   But by the end of 1967, Thomas Gold of Cornell and several other theoreticians had proposed natural models that seemed to explain the pulsar phenomenon very well. All of these models dealt with white dwarf or neutron stars. Using Occam's Razor, the more complex explanation of an interstellar civilization was dropped in favor of the natural-phenomenon explanation.
   (Ordinarily, science fiction people should be wary of glib technical explanations that pass by the possibility of other intelligences in space. Too often the scientists are merely whistling past the graveyard. But in this case, as you'll soon see, the natural explanation fits very nicely with the whole gravitational collapse/neutron star sequence. So the scientists might be right after all. This time.)
   
   
   
Fig. 7. The Ring Nebula in Lyra, presumably caused by a nova explosion that blew of some of the outer envelope of the central star.
   
   Gold's explanation seems to be the most widely accepted at present. He pictures the pulsar as a neutron star surrounded by fairly dense plasma clouds—the remnants of the core supernova, probably—with the whole complex of core and clouds held together by a strong magnetic field. If the neutron star is rotating, which it no doubt would be, its magnetic field's rotation would drag the plasma cloud around with it. However, the farther away from the star's surface you go, the faster the plasma must rotate to keep up with the forces pulling on it. This is like a "crack the whip" situation—tail-end Charlie must go like hell just to stay up with the rest of the gang.
   At a far-enough distance, the plasma simply can't keep up, even though it may be moving at speeds close to the speed of light. Part of the plasma breaks away from the magnetic field, and in the relativistic processes involved, a beam of radio energy is formed. This happens on every rotation of the neutron star, causing a regular periodicity to the radio pulses. The observed timing of the pulsars' radio bursts—all grouped around the once-a-second mark—fit in well with the expect spin rate of a 10-kilometer-wide neutron star.
   
   
   
Fig. 8. The famous Crab Nebula in Taurus, the result of a supernova in 1054 AD. The pulsar NP 0532 is at the center of the nebula, and is presumed to be a fast-rotating neutron star.
   
   Thorne prefers a different explanation. You recall that white dwarf stars may produce explosions on their simmering surfaces—sort of super-flares? Thorne believes that surface flares or explosions on a rotating white dwarf might explain the pulsars. The flares would emit a beam of radio waves as well as visible light. But this theory doesn't seem to explain the exactness of the pulsars' timing as well as Gold's.
   The discovery of the Crab Nebula pulsar brought enormous support to Gold's explanation. Here is exactly the situation he postulated: a neutron star imbedded in a plasma cloud laced with a strong magnetic field. Early in 1969 the Crab Nebula pulsar was detected visually, photographed, and even scanned by TV. The optical pulsations, in synchronization with the radio pulses, provided even further excitement and satisfaction for the astronomers.
   Moreover, for a few of the pulsars, the periods of pulsation are increasing. This most likely means that they're still shrinking, still being crushed to smaller size by gravity.
   How far can the crush go?
   The answer, according to theoretical physicists such as Thorne, is that under the right circumstances a star can literally go straight out of this universe.
   
   Let's take another look at a neutron star. With our eyes of theory we can see through the swirling carnage of plasma that surround the star.
   Originally a star of more than 1.4 solar masses, it has suffered a gravitational collapse, perhaps gone through either an outer envelope or core supernova—or both?—and now is reduced to a neutron core with a mass between one-fifth and twice the sun's mass. For several thousand years such a neutron star will emit more X-ray energy than the sun's output of visible light. And as we've seen, it's also causing radio and optical pulses, although these are most likely coming from the surrounding plasma clouds and not from the neutron star itself. After a hundred million years or so, the neutron star's temperature will cool down to a few thousand degrees and it will become a quiet, dark chunk of matter some 10 to 100 kilometers across.
   But if the neutron core of a collapsing star is more than twice the sun's mass, its gravitational infall won't stop at the neutron star stage. It will keep on shrinking. As the interior density goes past the ten billion tons per cubic inch mark, the neutrons themselves are squeezed down into smaller particles called hyperons. Classical physics can't describe what happens now, only relativistic physics can.
   To paraphrase an old joke, the star digs a hole, jumps in, and pulls the hole in after it!
   For once the gravitational collapse goes past the neutron star stage, the star is on a one-way ride to total oblivion. It will disappear from this universe.
   If the star's neutron core is more than twice the sun's mass, no possible braking force can stop the collapse. J. Robert Oppenheimer began studying this kind of ultimate gravitational collapse back in 1939, together with Hartland Snyder, of the University of California at Berkeley. Oppenheimer was soon diverted into the Manhattan Project and later into the ultimate tragedy of the McCarthy era. He never returned to this particular aspect of physics again. In fact, it wasn't until the mid-1960s, when the work on quasars and on supernova explosions both led to the problem of gravitational collapse, that the subject was really reopened for further examination.
    As the collapsing star squeezes in on itself; compressing the same amount of matter into a constantly-smaller radius, the gravitational field of the star becomes titanic. Photons emitted by the star must work against the gravitational field to escape the star's vicinity. We saw earlier that a body of 108 solar masses would have a gravitational field strong enough to produce large red shifts in the photons emitted.
   Now we're talking about single stars, of the order of the sun's mass. But, if the sun shrank down to a diameter of 5.8 kilometers, its gravitational field would be so strong that no photons could escape its surface. The sun would disappear.
   For a body of the sun's mass, the gravitational radius—the radius at which photons can no longer escape—is 2.9 kilometers. But the sun will never shrink that far, so the computer runs tell us.
   For a star with a neutron core of more than two solar masses, though—a black pit is waiting.
   It reaches neutron star density but keeps right on shrinking—gravity is so powerful that it overrides everything else. When the star's diameter gets down to about six kilometers, it winks out. Photons can't escape from it any longer. It has dug a black hole in space and disappeared into it.
   It's a strange place, this black hole. Because the gravitational collapse doesn't stop simply because we can't see the star anymore. According to theory, the star keeps collapsing until it reaches zero volume and infinite density! Such a point is called a Swarzschild singularity, after the German physicist Karl Swarzschild (1873-1916).
   More on the singularity aspect in a moment.
   
   We've watched a star collapse into the white dwarf stage, explode, and collapse into a neutron star. What would it look like if we could watch the final disappearance of a star as it collapsed down into a black hole?
   First, you'd have to be able to see through the plasma clouds that surround the scene. Second, you'd have to be able to see in X-ray wave lengths, because that's where the star's radiating. Finally, you'd have to look damned fast, for the whole thing happens in less than a second.
   The star visibly collapses and becomes "redder" as it shrinks. The photons must work harder and harder to get away from that fast-increasing gravitational field. Perhaps they're even shifted to visible wavelengths. But assuming you can see the star, regardless of the wave length of its radiation, one moment it's hanging there in the midst of its plasma nebulosity, then suddenly it shrinks like a pricked balloon, getting smaller and smaller.
   Then—still within the space of a second, remember—the collapse will seem to slow down. A few photons are struggling up out of the rim of that black hole. The star finally disappears, but there's a dim halo left, a few kilometers across, where those last few photons are taking tortuously spiraling paths to work out of the gravitational pit that the star has dug for itself.
   
   
   
Fig. 9. Thomas Gold's theory explaining pulsar radio emission calls for a fast-rotating neutron star with a strong magnetic field that forces part of the surrounding plasma cloud to rotate in step with the star itself At the distance where the plasma speed comes close to the speed of light, a bolt of plasma escapes and emits a radio pulse.
   
   The planets around such a star should be safe from falling into the gravitational pit, although any native life on such worlds would have been scoured away during the earlier explosions. We, in a spacecraft, can approach the star quite closely—as close as the gravitational radius itself—without being sucked into the black hole. The chances of losing interstellar spacecraft due to stray wanderings into invisible black holes are much smaller than the chances of being punctured by a millimeter-sized meteoroid in our solar system.
   Or are they?
   Gravitational collapse down into a black hole can also happen for objects larger than individual stars—for whole galaxies or quasars, in fact. The gravitational radius for a galaxy of a billion solar masses would be roughly one-fifth of an Astronomical Unit. With a diameter of some 15 million kilometers, you could fit several collapsed galaxies inside the orbit of Mercury! The gravitational effects on the rest of the solar system might be interesting—if gravitational waves from the collapsed galaxy can escape the black hole.
   Even an 0.2-AU "pothole" is microscopically small in the superhighway of interstellar space. But, if a craft should ever hit one, it will disappear forever.
   Or will it?
   
   In that strange world inside the black hole, where a star is crushed down to zero volume and infinite density, what physical rules apply? Even relativistic physics has nothing to say when the density gets to something like 1088 tons per cubic inch. This is 1079 times denser than a neutron star; if the sun were made that dense, its size would be about one millionth the diameter of an atomic nucleus. Nobody knows what happens, physically, down at the bottom of the black pit.
   Except that it might be bottomless.Or better yet, open-ended.
   Several theoreticians have pointed out that the mathematics of gravitational collapse and Swarzschild singularities apply only to perfectly spherical bodies. Stars are not perfect spheres, and certainly galaxies are even less so. As they're gravitationally crushed, it's likely that any deformations in their shapes will become exaggerated, not smoothed out. Roger Penrose, an English mathematical physicist, has shown that a nonspherical body may collapse down toward a singularity, but would not be completely crushed to zero volume.
   For reasons known but to the mathematicians, the body can escape going to a singularity. But it can't stay in the same physical location where it collapsed. In effect, it turns the black hole into a tunnel.
   You can visualize this by drawing on an analogy that relativistic physicists have often used. Picture space time as being represented by a thin, very flexible sheet of rubber. We'll picture it as a flat sheet, although actually it's probably curved and may be quite intricately convoluted. Massive bodies such as stars can then be thought of as tiny ball bearings resting on this rubber sheet. The bigger and heavier the star, the deeper the dimple it makes in the otherwise smooth sheet.
   For a star, or galaxy, that's collapsing into a black hole, this dimple starts to look more like a tunnel: a long, thin tube stretched in the fabric of space time by the gravitational collapse of a massive body.
   If' the body does not go down to a singularity, then the tube-tunnel might emerge somewhere else in space time. The star, or galaxy, has dug its way out of one place in the universe and reappeared somewhere, and perhaps sometime, else.
   No one has seriously proposed explaining the physics of this phenomenon. Where even relativistic physics breaks down, you can't expect more than a shrug of the shoulders when you ask questions. Perhaps the enormous energy locked in the star's gravitational field is the driving force behind its tunnel-drilling. Certainly, at the densities and gravitational field strengths involved, it seems clear that the entire fabric of space time gets badly bent. Dare one call it a space warp?
   Some cosmologists have seized on this idea to propose that the quasars are themselves the explosive reemergence of collapsed galaxies, bursting back into our universe with a loud, bright bang after having tunneled their way out of black pits.
   Maybe.
   But what are those tunnels like? Do they stay intact, a sort of underground railway system crisscrossing the fabric of space? Could a spacecraft take a shortcut, and maybe break the universal speed limit by going through a tunnel? What happens to time inside of a tunnel?
   Ultimately, if the universe is finite, its expansion will slow down, stop, and the final gravitational contraction will begin. Will the universe end in a black pit? Or will we—all squeezed down to hyperons at least—tunnel out into a new and different universe?
   Whichever way it goes, it's a long time in the future. For the present, it's fun to consider the possibilities of tunnels through space. Far from avoiding black holes, someday our spacecraft may be seeking them out, looking for the Northwest Passage between here and the Clouds of Magellan. ? 
   
   
   
     The results of a star's gravitational collapse depends on the mass of the collapsing body. For stars of the sun's mass, electron compression will halt the eventual collapse at the white dwarf stage. For bodies of up twice the sun's mass, the collapse will produce a neutron star. For bodies of more than twice the sun's mass, the collapse is irretrievable: the star will disappear from this universe.