Black holes are hot. Although this is literally true (according to the latest theories) of some black holes, I mean they are hot as a topic. The above books are only fragments of this year’s crop that deal entirely or in part with black holes. Why such obsessive interest in astronomical objects that may not even exist, and that in any case cannot be fully understood without knowing general relativity theory and quantum mechanics?

Let the first paragraph of Isaac Asimov’s book set the tone for what I believe is the answer.

Since 1960 the universe has taken on a wholly new face. It has become more exciting, more mysterious, more violent, and more extreme as our knowledge concerning it has suddenly expanded. And the most exciting, most mysterious, most violent, and most extreme phenomenon of all has the simplest, plainest, calmest, and mildest name—nothing more than a “black hole.”

Black. Black is beautiful, black is ominous, black is awesome, black is apocalyptic, black is blank. “A hole is nothing,” Asimov continues, “and if it is black, we can’t even see it. Ought we to get excited over an invisible nothing?”

Nothing. Why does anything exist? Why not just nothing? This is the super-ultimate metaphysical question. Obviously no one can answer it, yet there are times (for some people) when the question can overwhelm the soul with such power and anguish as to induce nausea. Indeed, that is what Sartre’s great novel, Nausea, is all about.

Suddenly we are being told that if a star is sufficiently massive it eventually will undergo a runaway collapse that ends with the star’s matter crushed completely out of existence. Not only that, but our entire universe may slowly stop expanding, go into a contracting phase, and finally disappear into a black hole, like an acrobatic elephant jumping into its anus. There is speculation (not taken seriously by the experts) that every black hole is joined to a “white hole”—a hole that gushes energy instead of absorbing it. The two holes are supposedly connected by an “Einstein-Rosen bridge” or “wormhole.” When a huge sun collapses into a black hole, so goes the conjecture, a companion white hole instantly appears at some other spot in spacetime. This could explain the incredible outpouring of energy from the quasars, those mysterious objects, apparently far beyond our galaxy, that nobody yet understands. Was the big bang which created our universe the white hole that exploded into existence after a previous universe collapsed into its black hole?

It is easy to understand why the religiously inclined are excited by such wild, speculative cosmology. The heavens declare the glory of God and the firmament showeth his handiwork. Nor is it hard to understand why those who are into Eastern philosophy, pseudoeastern cults, parapsychology, and unorthodox science are also fascinated. If the universe can be that crazy, so goes the argument, then why be disturbed when the Maharishi announces, as he recently did, that transcendental meditation can enable one to levitate and become invisible? Black holes are the latest symbols of unfathomable mystery. Public interest in them is, I am persuaded, no indication of interest in science, but rather a peculiar byproduct of the specter of the supernatural that is now haunting North America.

For the reader with no understanding of relativity and quantum theory—that is, the average reader—Asimov’s book is the best of the lot. The old maestro writes with his unfailing clarity, humor, informality, and enthusiasm. Like all top science-fiction writers he knows exactly where to draw the line between serious science and fantasy. Periodically he reminds his readers that there is as yet no clear observational evidence that black holes exist, and that “almost anything some astronomers suggest about a black hole is denied by other astronomers.”

Cautiously, step by step, Asimov sketches the necessary background for understanding a black hole’s properties. He begins with gravity, that gentle, all-pervasive, poorly understood force that holds together the matter of galaxies, stars, and planets. At the centers of planet-size bodies the pressure of gravity is insufficient to overcome the opposing electromagnetic force that binds the molecules of the matter at the core, and the matter remains intact. However, if the body is large enough (about the size of Jupiter) the pressure of gravity becomes so strong it triggers a hydrogen fusion reaction. The body becomes a sun.

There are three ways a sun can die. If a star is close to the size of our sun it will exhaust its hydrogen fuel, expand to a red giant, then slowly contract to a white dwarf. Eventually it will cool to a black dwarf, a permanently embalmed corpse that never changes unless it happens to be eaten by a black hole.

If a star is moderately greater in mass than our sun, its fate is more interesting. It is likely to explode into a supernova; then part of its mass instantly shrinks to a size smaller than the earth. So great is the density of this body that its gravitational force overcomes the opposing electromagnetic force and the structure of the star’s matter disintegrates. It becomes a fast-spinning neutron star.


Most astronomers are convinced that pulsars are neutron stars. These are small stellar objects inside our galaxy that send out absolutely regular beeps of radio waves, sometimes beeps of visible light. There are probably millions of them in the Milky Way that are within the range of today’s radio telescopes.

If a star is much more massive than our sun, it is expected to expire in a manner so bizarre that its fate is still shrouded in mystery. After it completes its catastrophic implosion, not even neutrons can withstand the enormous gravitational compression. All particles are totally destroyed, and the laws of physics no longer have meaning. The star has entered a black hole.

Black holes were crudely anticipated in 1798 by the French mathematician Pierre Simon de Laplace. His predecessor Isaac Newton believed that light consists of particles that are affected by gravity. If a star is large enough, Laplace pointed out, its gravitational force will prevent all light from escaping from it. This is not strictly true. In Newtonian physics the speed of light approaching a star, no matter how massive, would be so greatly accelerated that it could bounce off a reflecting surface and escape.

In relativity theory, light also consists of particles (photons) that are influenced by gravity, but their speed is a constant that cannot be exceeded. A few months after Einstein published his general relativity theory a German astronomer, Karl Schwarzschild, made exact calculations of what is now called the “Schwarzschild radius.” This is the radius of a body, given its mass, below which gravity is strong enough to prohibit light, matter, or any kind of signal from escaping. It is the critical radius below which matter becomes an invisible black hole. For a mass equal to our sun’s, the radius is a few kilometers. For a mass equal to the earth’s, it is the radius of a large pea.

In 1939 J. Robert Oppenheimer and his student Hartland Snyder made some surprising calculations. Assuming the truth of relativity, there are no laws to prevent the gravitational collapse of a sufficiently massive sun from compressing the sun’s matter within the Schwarzschild radius and forming a black hole. Moreover, the calculations lead to something even more mind boggling. At the core of every black hole there has to be a spacetime “singularity”—a term mathematicians use for a point at which something catastrophic happens to the solution of an equation. In this case, calculations show that spacetime curvature becomes infinite, which is to say that it becomes a single point. At that point, gravitational force and density (mass per unit volume) also become infinite.

If a spacetime singularity actually occurs and can be observed, it is called a “naked singularity.” So far, no one has seen a naked singularity. Perhaps its equations tell only part of the story and there are forces not yet understood which prevent singularities from existing. Roger Penrose, a brilliant theoretical physicist at Oxford University and a chief architect of black holes, believes that spacetime singularities can occur, but a “cosmic censor” prevents them from becoming naked. It conceals them, so to speak, inside an “event horizon” that prevents them from interacting in any way with the universe.

For twenty years the calculations of Oppenheimer and Snyder were considered no more than eccentric exercises for graduate students. Then in 1962 the quasars were discovered, and five years later the pulsars. Suddenly astrophysicists realized that maybe they were seeing objects in the final stages of just the sort of catastrophic collapse that had been worked out on paper. At first it was hoped that if the collapsing mass of a big star were a bit lopsided, the singularity could be avoided. But Penrose proved otherwise. The singularity is unavoidable. Regardless of the size, shape, or chemical constitution of a sun, if it is massive enough to collapse into a black hole, it will have that awful singularity at its center. As for the hole itself, all the structural peculiarities of the sun that formed it will be obliterated. “Black holes have no hair,” so goes a theorem. It means that all black holes, aside from mass, spin, and electric charge, are identical.

It is possible, as Philip Morrison and other cosmologists have emphasized, that laws not yet known may prevent the formation of black holes. True, there are some spots in the sky where astronomers think they see something going on that can be explained only by a black hole—notably the strong X-ray radiation coming from the vicinity of a giant star in the constellation of Cygnus (the Swan)—but what they see may have conventional explanations. There is no hard evidence, though the prevailing opinion is that black holes do exist. Some astronomers suspect that a giant black hole squats at the center of every galaxy, spinning silently while it slowly gobbles up nearby suns. As of today, however, black holes are theoretical constructions supported mainly by the fact that relativity theory requires them, by the rule that anything not excluded by theory probably exists, and by observed phenomena in the heavens that cannot be explained in any better way. Either black holes are real, it is said, or there are holes in relativity.


There is, of course, nothing wrong in building theoretical models for structures before they are observed. Sir Arthur Stanley Eddington once remarked, only half in jest, “You cannot believe in astronomical observations before they are confirmed by theory.” Eddington, by the way, a few years before Oppenheimer’s calculations, came remarkably close to constructing a model of a black hole.

“The star,” Eddington wrote, “apparently has to go on radiating and radiating and contracting and contracting until, I suppose, it gets down to a few kilometers radius, when gravity becomes strong enough to hold the radiation, and the star can at last find peace.” So far, so prophetic! But Eddington went on: “I felt driven to the conclusion that this was almost a reductio ad absurdum of the relativistic degeneracy formula. Various accidents may intervene to save the star, but I want more protection than that. I think that there should be a law of nature to prevent the star from behaving in this absurd way.”

It is too early to know whether Eddington’s conclusion is right or wrong. In a few years astronomical evidence for black holes may be overwhelming. Or it could go the other way. Today black holes are the fashionable playthings of clever astrophysicists. Tomorrow their models may collapse to take their places alongside phlogiston and the epicycles of Ptolemy.

The most sensational of recent conjectures is that our entire expanding universe is destined to enter a black hole. If there is enough matter in the universe (much of it could be hidden inside black holes), gravity will halt the expansion and the universe will start going the other way. Cosmologists can think of nothing to prevent this collapse from plunging the cosmos into a black hole. As for what happens next, who knows?

Readers who want to go more deeply into the structure of black holes will find Robert Wald’s book a worthy purchase. He is a physicist at the University of Chicago’s Fermi Institute, and his book is based on a series of lectures he gave at the university in 1976. It covers the same ground as Asimov’s book, but with more technical information. The last chapter is particularly good in summarizing the recent discoveries of the young Cambridge mathematical physicist, Stephen Hawking.

Hawking’s combination of courage, optimism, and intellectual virtuosity is already legendary. For years he has been almost totally paralyzed by a progressive nerve and muscle disease. Although he can move himself about in a motorized wheelchair, he cannot write, and he speaks with enormous difficulty. But his mind still operates with crystal clarity, and his calculations are still staggering his colleagues.

Hawking’s major discovery is that black holes are not black. Quantum theory, it turns out, implies that in the powerful gravitational field surrounding a black hole there is constant creation of particles (of every kind) and their antiparticles. Some of these particles fall into the hole, others escape as radiation. There is thus a constant leakage of energy, and a flux around the hole that could be observed.

If black holes are large, this loss of energy is slow and negligible. Hawking believes, however, that the big bang may have been chaotic enough to have fabricated billions upon billions of micro black holes, each smaller than a proton, but containing a mass of a few hundred million tons. These “primeval” miniholes would now be in their final stages of evaporation. They would get hotter and hotter, smaller and smaller, and finally explode in a tremendous burst of particles and gamma rays.

Nigel Calder’s big, handsome volume devotes only two chapters to black holes, but they are excellent nontechnical summaries, and the other chapters are a splendid introduction to the latest theories of matter. Calder is one of the most reliable of British science writers. His book, based on a popular BBC television show which he wrote and presented last January, is abundantly illustrated with diagrams and photographs, including pictures of famous physicists whose faces the public seldom sees.

Calder is unusually skillful in explaining quark theory and why it is rapidly outrunning its nearest rival, the “bootstrap” theory. The bootstrap hypothesis is the “democratic” view that none of the particles that make up matter is more fundamental than any other. Each is simply an interaction of a set of other particles. The entire family thus supports itself in midair like a man tugging on his bootstraps, or a transcendental meditator in the lotus position, suspended a few feet above the floor.

Quark theory is the aristocratic view that particles are combinations of more elementary units which Murray Gell-Mann named quarks after the line in Finnegans Wake, “Three quarks for Muster Mark!” At first only three kinds of quarks were believed necessary: up, down, and strange, together with their antiparticles. The three kinds are called “flavors.” There are now reasons for thinking there is a fourth flavor, “charm.” Each flavor comes in three “colors.” In the US the colors naturally are red, white, and blue. (Calder’s plates use red, blue, and green, with turquoise, mauve, and yellow for the anti-colors.) This makes twelve quarks in all, with their twelve antiquarks.

Color and charm are, of course, whimsical terms unrelated to their usual meaning, although the mixing of quark colors does obligingly correspond (as Calder shows) to the mixing of actual colors. Some theorists think there are still other quark properties such as truth, beauty, and goodness. Abdus Salam, the noted Pakistani physicist, is now promoting a “quark liberation movement” that regards quarks as made of “pre-quarks” or “preons.” In Peking a group of young physicists have a similar view involving “stratons” that form an infinite nest like a set of Chinese boxes.

The essences of these debates are skillfully outlined in Calder’s book. He even leads you to the brink of the new, exciting “gauge theories” that may someday unify the strong, weak, and electromagnetic forces—perhaps even gravity—in one fundamental theory.

P.C.W. Davies’s book, although it too contains an excellent account of black holes, is mainly a summary by a British physicist of modern views about space and time. Davies has long been troubled by why events in our universe go only one way in time. His earlier book, The Physics of Time Asymmetry, was fairly technical. This volume covers the same ground, but on a level more readily understood by laymen.

Time has at least five different “arrows”:

  1. The arrow of psychological time—our consciousness of the flow of events from past to future.
  2. The arrow of certain weak interactions involving K mesons. All other particle interactions are “time reversible” in the sense that, if you take a motion picture of them and run it backward, you see nothing to indicate the film has been reversed. The K-meson events, inexplicably, violate this reversibility.
  3. The arrow of entropy—the movement of macrosystems such as galaxies toward increasing disorder (comparable to the destruction of order in a deck of cards by random shuffling).
  4. The arrow of radiation from a center, such as the expanding concentric circles produced by a stone dropped into a pond, or the radiating light of a sun.

  5. The monstrous arrow of the expanding universe.

How these five arrows are related to one another, and whether universes can exist with one or more (perhaps all) arrows pointing the opposite way from those of our own universe, is a singular story, nowhere better told than in Davies’s book.

Fred Hoyle’s volume is the latest of his seemingly endless popular surveys of modern astronomy, all lavishly illustrated and entertainingly written. Hoyle likes to beat loudest on the drums of his own inventions, but it doesn’t matter because his speculations are never boring. It must have been a tragic experience for him to watch his beloved steady-state theory of the universe go down the drain as the big bang theory became accepted, but this seems not to have diminished his mental energy or his fondness for funky theories. Hoyle’s book has less to say about black holes than the others, but this is because it cuts a broader swath. The book includes chapters on earth geology, on biology, and on the importance of population control. (He sees the unchecked growth of population as the greatest of all threats to humanity.)

Our two remaining books, entirely about black holes and related matters, plunge into unrestrained fantasy. Adrian Berry, science writer for a London newspaper, makes only a feeble attempt to separate fact from reasonable conjecture, or reasonable conjecture from eccentric conjecture. His book is best read as you would an Asimov science-fiction novel. Indeed, some of Asimov’s novels anticipate much of what Berry has to say.

Berry is concerned mostly with the conjecture that every black hole is joined by a wormhole to a white hole in some other part of the cosmos, or to a white hole in a completely different cosmos. Perhaps the “other” world is made of antimatter, like the Antiterra of Nabokov’s novel Ada. Matter pours into our black holes to emerge as antimatter in the other world’s white holes, while its antimatter pours into its black holes to emerge from our white holes.

Some recent calculations have suggested that a spaceship just might be able to rocket into a black hole and avoid hitting the dreadful singularity. Berry imagines a future in which spaceships use black and white holes as entrances and exits for instantaneous travel across vast distances. When this becomes possible, he writes, mankind will be able to roam and colonize the entire universe. Science fiction heroes have been doing this for decades, but Berry dresses it up in the latest jargon, and his book is fun to read if you don’t take it seriously.

John Gribbin’s book on white holes carries this kind of fantasy to still greater heights. Indeed, his book is almost as funny as John G. Taylor’s Black Holes, published in 1973. Taylor is the mathematical physicist at the University of London whose latest book, Superminds, is about British children whom Taylor is convinced can bend spoons by paranormal powers better than Uri Geller’s. The psi force is probably electromagnetic, Taylor argues. His black hole book is less preposterous, but it does use the black hole as a jump-into point for occult speculations.

Gribbin, who has a doctorate in astrophysics, is the co-author of an earlier book of quasi-science, The Jupiter Effect. This great work explains why “there can be little doubt” that in 1982 Los Angeles will be the site of “the most massive earthquake experienced during this century.” In 1982 all nine planets will be on the same side of the sun. Jupiter’s pull on the sun will thus be augmented by the other planets. This will cause unusual sunspot activity which will agitate the earth’s atmosphere. This in turn will agitate the earth’s crust, especially along the San Andreas fault. “There can be little doubt” is the phrase that should have forewarned the good Dr. Asimov before he wrote his introduction to this book.

The most absurd passage in Gribbin’s new book, the one on white holes, speculates on how tachyons may explain psychic spoon bending. Tachyons are conjectured particles that go faster than light. There is not the slightest evidence they exist, but if they do they would, for certain observers, move backward in time. “Perhaps,” writes Gribbin,

the spectacular production of the bent spoons produces the wave of astonishment from the audience, releasing a flood of tachyons which travel backward in time to cause the spoons to bend just before they are produced to cause the surprise. If such a process could be triggered deliberately, it would explain telepathic phenomena as the direct tachyonic communication between minds, but something as physical as spoon bending seems to require the pooled effort of many minds—except, according to John Taylor, in the case of children. This should be no surprise in the light of the above; children have more vivid imaginations than most adults, with more powerful emotions presumably releasing stronger tachyonic vibrations. Perhaps this tachyonic link even provides a clue to such mysteries as poltergeists!

Black holes and bent spoons. The healthy side of the black-hole craze is that it reminds us of how little science knows, and how vast is the realm about which science knows nothing. The sick side of the black-hole boom is the appropriation of astrophysical mysteries to shore up the doctrines of pseudoscientific cults, or the shabby performances of psychic rip-off artists.

Penrose is now doing research and publishing papers on a bizarre mathematical entity he has invented, called a “twistor,” that he hopes will clear up some thorny problems about the linking of gravity and quantum theory. A twistor is a type of “spinor,” a mathematical operator that calculates what happens when rotations are combined. Penrose’s twistors are sort of halfway between particles and pure geometry. I wouldn’t be surprised to learn that even now some hack journalist is working on an article for Reader’s Digest titled “Twistors: Cosmic Carriers of Psychic Energy?” With a little help from the media, twistors could become hotter than black holes.

This Issue

September 29, 1977