Those Baffling Black Holes

"What did it look like?" "Like--like--It had the biggest head you ever saw... A huge great enormous thing, like--like nothing. A huge big--well, like a --I don't know--like an enormous big nothing..." --A.A. Milne, Winnie-the-Pooh (1926)

In Milne's classic, Piglet was left virtually speechless by his run-in with what he thought was the mysterious Heffalump. Now astronomers can share his bafflement as they grope for words to describe their own strange encounter. Off in the distant heavens, among a grouping of stars that the ancients called Cygnus (the Swan), they seem to have found a celestial version of a Heffalump. It is a cosmic beast of such enormous gravity that it appears to be tugging, stretching and, indeed, slowly gobbling up its giant companion, a massive star more than 20 times the size of the sun. Like Milne's fantasy, it is a huge, great, enormous, big nothing. In the catchy phrase of retired Princeton Physicist John Wheeler, it is a black hole in space.

A black hole? The name is highly appropriate. Nothing--not even light--can escape from black holes, making them invisible. Even more astounding, these bizarre non-objects are in effect celestial vacuum cleaners that voraciously devour everything they meet. They are bottomless pits into which atomic particles, dust and giant suns all disappear without a trace. They are rips in the very fabric of space and time, places where long-cherished laws of nature simply do not apply. So unbelievable and paradoxical are these notions that they have led to what Wheeler calls "the greatest crisis ever faced by physics." Says he: "Never before did we think that matter could be so ephemeral."

If whole stars can vanish from sight within black holes, literally crushed out of existence, where has their matter gone? To another place and another time? Where did it come from? In searching for answers to the fundamental questions raised by black holes, scientists are infringing on the realm of philosophers and theologians. They are trying to find the meaning of life, of being, of the universe itself.

Even in an age that has witnessed everything from the harnessing of the atom to flights across the solar system, the thought of matter going down a kind of cosmic drain stretches the mind. It is totally at odds with common sense and, a cynic might say, smacks slightly of selfdelusion, if not madness. After all, the frightful Heffalump turned out to be only Pooh with his head stuck in a jar of honey.

Are black holes science's Heffalumps? Absolutely not, insist black-hole theorists, who are among today's best and brightest scientific minds. In fact, they say, the universe probably teems with these bizarre apertures.

Says Caltech's Kip Thorne: "There may be more than a million black holes in our galaxy alone."

On the surface, that seems to be a rather audacious claim. Even through the most powerful telescope, no one has seen--or ever will see--black holes. Thus, for the time being at least, these inkblots of space are mere mathematical figments. So far, they can be shown to exist only as solutions to the complex equations of general relativity--Einstein's theory of gravity--and very troubling solutions at that.

If Einstein's theory is correct, black holes are the natural consequences of the death of giant stars. In what astronomers call catastrophic gravitational collapse, most of the matter contained in such a dying star begins falling in toward the stellar center. If the conditions are right, the matter crushes together with such enormous force that it literally compresses itself out of existence. The star becomes what mathematicians call a "singularity." Its matter is squeezed into an infinitesimally small volume, and it simultaneously becomes infinitely dense and has an infinitely high gravitational force. At the point of singularity, time and space no longer exist. "Imagine," says Harvard Astrophysicist Jonathan Grindlay, "you take an enormous mass and shrink it down to nothing. A very disturbing idea."

Scientists have good reason to be disturbed--and excited --by the idea. For many centuries, astronomers thought of the universe as quiet, serene and essentially unchanging. Now it is known to be the scene of incredible violence--of exploding galaxies and stars, of prodigiously energetic quasars, a universe that still literally reverberates from its fiery birth. Many scientists are all but convinced that black holes lie at the root of many of these awesome events. They are fascinated and somewhat frustrated by the fact that the immense gravity of black holes prevents any escape from them. As a consequence, says Harvard Physicist Larry Smarr, "there are parts of the universe from which, in principle, we cannot get any information."

When they are confronted with such a situation, scientists are often inclined to toss out the suspect equations, along with the physical theories underlying them. Yet general relativity has withstood many other tests since it was devised by Einstein more than half a century ago, and more and more scientists believe that the evidence in the skies is rapidly piling up in favor of the reality of black holes.

Besides the possible black hole in Cygnus, one appears to be part of another double-star system in the constellation Scorpius (the Scorpion). Three more may have been detected, each at the heart of a globular cluster of stars in the halo of the earth's Milky Way galaxy. In the inner regions of these clusters, which contain tens of thousands of individual stars, some of the stars are revolving with wobbly motions, as if disturbed by a center of enormous gravity. Herbert Gursky and Andrea Dupree of the Harvard-Smithsonian Center for Astrophysics believe that these stars "may well be orbiting a black hole with the mass of a thousand suns." Still other candidates lie far beyond the Milky Way. At least two galaxies, known as M87 and NGC6251 in astronomy catalogues, seem to be undergoing violent upheavals, quite possibly because of black holes inside them.

While black holes may be hard to sight in the heavens, they are gaining high visibility on earth. They are the current rage of astrophysics, a marriage between the older disciplines of astronomy and physics. Says Astrophysicist W. David Arnett of the University of Chicago: "Black holes are where it's happening these days." Hardly a week passes without the publication of some jarring new conclusion or insight about black holes in the scientific journals. In one of several scientific meetings that considered black holes this summer, some 70 specialists gathered in Seattle for twelve days of cosmic discussion. One of their primary preoccupations was finding new ways of locating and identifying the elusive beasts, admittedly a difficult task. Says Princeton Astrophysicist Jeremiah Ostriker: "The state of our art is as though you could only taste a substance and not see, smell or hear it."

Scientists are not the only ones smitten by black-hole fever. The parcels of nothingness are a favorite topic on the lecture circuit. They bring out record crowds for planetarium shows, and they have lately been the theme of a spate of books. In the popular lexicon, the term black hole once suggested only the legendary hellish cell in Calcutta in which British prisoners were held by an 18th century Indian nawab. Now it has become an immediately recognizable catchword for a different kind of darkness. Says one young astrophysicist:

"When I announce my profession at a cocktail party, I can almost hear the yawns. When I say that I study black holes, everyone instantly perks up."

As a pop cultural phenomenon, black holes also appear in slogans on T shirts and bumper stickers (BLACK HOLES ARE OUT OF SIGHT), and are the subject of banter by Johnny Carson and other TV talk show hosts. A gag advertisement in the sci-fi magazine Analog by a company named Nothingness Unlimited promoted "black-hole disposal units," invisible devices (in seven decorator colors) that suck up unlimited waste.

The University of Chicago's noted Indian-born astrophysicist, Subrahmanyan Chandrasekhar, when hospitalized for heart surgery, found to his delight that all his doctors and nurses seemed to want to talk about was black holes. The White House also recognizes the gravity of black holes. Upon reading a news article about them one morning, President Carter promptly asked his science adviser, Frank Press, for his thoughts. Press, whose son William happened to have done research on black holes, sheepishly confessed ignorance, explaining that he could not get through the paper so early in the day.

To some extent, the public's passion for black holes is part of the faddish craze for the likes of parapsychology, the occult, UFOs, thinking plants, von Daniken and other pseudoscientific hokum. Says one astrophysicist: "For some people, black holes seem to be the Bermuda Triangles of space."

Perhaps the most compelling reason for the widespread interest is that black holes seem to mark the point where astrophysics intersects metaphysics and science finally converges with religion. Indeed, black holes seem to have universal implications, for the gravitational collapse of stars suggests that the universe, too, can begin falling back in on itself. If that happens, its billions of galaxies will eventually crush together and could form a super black hole. And what then? Nothing? Or would a new process of creation somehow begin?

Defining a black hole for a layman taxes the imagination and vocabulary of even the most articulate scientist. The matter that formed the hole has long since disappeared, like Alice in Wonderland's Cheshire cat, leaving behind only the disembodied grin of its gravity. From afar, that gravity has the same effect on objects in space as it did when its matter existed. But closer in, the gravitational force soars, becoming so great that it prevents the escape of light.

The boundary marking that no-escape distance depends on the mass of the deceased star. Typically, this frontier is an imaginary sphere tens of kilometers across that defines the size of the black hole. It is the point of no return that scientists call the black hole's "event horizon." Anything crossing this border would be stretched spaghetti-thin, pulverized by gravitational tidal forces, and sucked into the singularity. To an observer outside--say an astronaut watching his abandoned craft plunge into the black hole--the result would be different. Because of relativistic effects, the spacecraft would appear to move ever more slowly, and closer and closer to the event horizon, without ever reaching it.

Black holes apparently come in both economy and giant sizes. The gifted British theoretical physicist Stephen Hawking has shown mathematically that tiny black holes, dating back to the very origins of the universe, could exist. In the Big Bang, the primordial explosion that created the universe some 15 billion to 20 billion years ago, matter was hurled in all directions. In some places, Hawking says, quantities of matter roughly equivalent to the amount in a mountain may have become compressed enough to collapse, forming what he calls mini-black holes. Their circumference, as measured by their event horizons, could be no larger than that of an atomic particle.

Subsequently, two imaginative University of Texas researchers suggested that a tiny black hole had passed through the earth in 1908, causing the mysterious blast that leveled trees for miles around in the Tunguska region of Siberia. But most scientists doubt that explanation. Says Princeton's Ostriker: "A hit by a mini-black hole would have blown up the entire earth."

In an even more brilliant mathematical tour de force, Hawking has gone on to point out that black holes apparently violate the cherished no-escape doctrine. Contrary to expectations, Hawking's mini-black holes are gradually "evaporating," leaking subatomic particles and high-energy gamma rays back into the universe and rising in temperature. After billions of years, according to Hawking's calculations, the minuscule hole, unlike its large brother, can no longer sustain the buildup of heat and expires in a Gotterdammerung-like blast comparable to the explosion of millions of H-bombs.

Incredible as it may seem, scientists are now postulating supergiant black holes as well, monsters with event horizons millions of miles across and formed from a mass equal to that of billions of suns. Observations with the big telescopes at California's Palomar and Arizona's Kitt Peak National observatories strongly support the likelihood that at least one such heavyweight exists in M87, a galaxy that appears to be spewing out a great jet of matter. Astronomers found that M87's center is ten times as bright as the rest of the galaxy, and is surrounded by stars orbiting at unexpectedly high velocities. To provide the gravitational power plant for this galactic vortex, Cambridge's Martin Rees posits a black hole 5 billion times as massive as the sun in M87's core.

Perhaps because of a philosophical or psychological reluctance to accept the finality of black holes, some scientists speculate that matter going down these drains may not always be destroyed. On the contrary, under special circumstances the matter might be conducted by a rapidly rotating black hole through space and time via passages dubbed wormholes. It would reemerge in a different part of the universe or perhaps in another universe entirely. Some scientists have even said that black holes may be linked to weird opposites called white holes. Located elsewhere in space and time, these would disgorge matter rather than consume it. For a while, it was thought that those inexplicably bright and energetic objects known as quasars might actually be white holes, spewing out matter and energy from another universe or from another part of this one.

Now scientists suspect that quasars, so distant that their light takes billions of years to reach earth, are galaxies in an early and violent stage of evolution.

If the universe were indeed laced with magical conduits, could they perhaps be used some day to overcome the overwhelming distances between the stars and galaxies? One enthusiastic British science writer, Adrian Berry, has predicted that in a few centuries an advanced civilization might create its own black hole at a safe distance away (by sweeping up enough interstellar debris with magnets and letting it compress under its own gravitation) and then use it as a portal to other worlds. Scientists generally dismiss such fantasies with a bemused shrug. Even if adventurous travelers could survive the plunge into a black hole, the rest of the trip might still be far-out, to say the least. Because black holes play relativistic tricks with time, a space traveler who entered one and came back via a wormhole might find himself returning to his place of origin before he left it. Thus in theory he could see himself as he was about to depart. Explains Cambridge's Bernard Carr: "There are mathematical solutions that allow these kinds of things. The question is whether they are physically realistic."

The mathematics of ordinary black holes, if such concepts can be called ordinary, rests on firmer theoretical ground. As early as 1796, the French savant Pierre Simon de Laplace anticipated black holes in a rough way, using only Newtonian ideas about gravity and light. If a star were really massive, he calculated, the force of gravity at its surface would be enormous. The star's escape velocity--the speed it takes to free an object like a spacecraft from a heavenly body--might exceed the speed of Newton's "corpuscles" of light. Thus the particles could not leave the star. Concluded Laplace: "The largest luminous bodies in the universe may be invisible."

No one bothered to look further into Laplace's dark stars until Einstein shook the scientific world more than a century later with his general theory of relativity. Newton had pictured gravity as simply a force exerted by one body upon another: this attraction was directly proportional to the masses of these bodies and inversely to the square of the distance between them. In the new Einsteinian view, however, gravity became more complex. It curved both space and time, almost as if heavenly bodies like the sun sat in the middle of a huge rubbery membrane and depressed it. The pathway of anything caught on this sloping surface--a passing spacecraft, a planet, or even something so seemingly ethereal as a ray of starlight--would curve toward the object in the center.

In 1915, shortly after Einstein formulated his theory, a German colleague named Karl Schwarzschild considered one of general relativity's consequences. If a star were to become sufficiently compact and dense, Schwarzschild found, its gravity would so warp space and time around it that the star would literally enclose itself. For a celestial body of the sun's mass, the critical radius turned out to be about 3 km (2 miles). If the star shrunk beyond that, it would vanish. This so-called Schwarzschild radius, or event horizon, is in effect the black hole's boundary. Any matter crossing it simply disappears.

Unlike Laplace's dark star, this Einsteinian black hole--the name was not coined by Physicist Wheeler until the 1960s--had far more finality. Since relativity forbids anything to move faster than light, an idea unknown in classic Newtonian physics, escape was impossible. All the energy in the world could not extract an object from a black hole.

Astronomers now realize that the life history of a star is essentially a tug-of-war between two powerful competing forces. On the one hand, there is the great outward pressure on the star's gases created by radiation and heat from its internal fires. On the other, there is the inward pull of the star's gravity. In a star like the sun, the battle between radiation and gravity is long stalemated; the sun has been shining for some 5 billion years and will remain relatively unchanged for another 5 billion. After the star exhausts most of the hydrogen near its core and begins to burn hydrogen in its outer regions, it swells into a red giant. When the sun reaches this stage, its hot gases will envelop Mercury, Venus and the earth.

Using Einstein's equations, astronomers determined that after all of the nuclear fuel is consumed, gravity eventually would cause the star to contract into a white dwarf, a sphere only about as big as the earth but so dense that each cubic centimeter would weigh a ton. Their calculations finally made sense of a dim companion of the star Sirius that was first observed in the 1860s and had puzzled astronomers for decades. Though the star was apparently small, it exerted an inexplicably great gravitational pull on Sirius. The dense little companion--like others that have been observed since--was a white dwarf. But would bigger stars, with greater gravity, shrink into still smaller, even more dense bundles?

Preoccupying himself with this problem while traveling by ship from India to England to take up studies at Cambridge in the early 1930s, the young Chandrasekhar came to an astonishing conclusion. His calculations showed that if a star is larger than 1.4 times the mass of the sun when it begins its collapse, it will compress to a state even more dense than that of a white dwarf. How far could the star collapse? In one of the great understatements of modern science, Chandrasekhar would only say: "One is left speculating on other possibilities."

Surely, replied the illustrious British astronomer and physicist Sir Arthur Eddington, nature would forbid such a reductio ad absurdum as a star so compressed that sit does not shine. But two other astronomers, Mount Wilson Observatory's Fritz Zwicky and Walter Baade, were more intellectually adventurous. Though no similar event had been seen in the Milky Way since 1604, they had observed in other galaxies great stellar explosions called supernovas. These occur when massive dying stars, like giant springs, rebound from their calamitous collapse. For days or weeks such exploding stars may shine as brightly as all the galaxy's billions of stars combined. Zwicky and Baade felt sure that the force of such a gravitational collapse and explosion could not only spray material far off into the heavens, but also actually crush the very atoms in the core of a star. Orbiting electrons would be pounded right into the atom's nucleus and wedded with its protons. The result of this celestial alchemy, they said, would be a clump of solidly packed neutrons.

Zwicky and Baade even suggested a possible location of such a neutron star. They predicted that one might be found in the center of the expanding gases of the celebrated Crab Nebula, the site of a Milky Way supernova that was observed by Chinese astronomers in A.D. 1054.

Hardly any of Zwicky and Baade's colleagues took the proposal very seriously, but some theoretical physicists did follow up the idea. One of these was a young professor named J. Robert Oppenheimer at the University of California at Berkeley, who was studying Einstein's equations as they applied to gravitational collapse.

In the late 1930s, on the eve of World War II, Oppenheimer published two landmark papers in the journal Physical Review. The first, in collaboration with a graduate student named George Volkoff, argued that neutron stars could in fact exist. They would have a diameter of about 10 km (6 miles) and weigh about 10 million tons per cu. cm. In the second paper, innocuously titled "On Continued Gravitational Contraction," Oppenheimer and another student, Hartland Snyder, contended that if the dying star was massive enough, nothing in Einstein's theory stood in the way of the ultimate compression--the formation of a singularity.

All this was, of course, just theorizing, what Einstein called "thought" experiments. Conditions needed to form anything like a neutron star, to say nothing of a black hole, could not be duplicated on earth. Besides, the outbreak of the war forced scientists to turn to more pressing matters. Oppenheimer soon went off to direct the building of the first atomic bomb, and the concept of total gravitational collapse was largely forgotten until after the war.

By then astronomers had turned their wartime technology to the peaceful pursuit of stargazing. Rockets equipped with X-ray detectors roared off the pad. Soaring high above the atmosphere, which prevents celestial X rays from reaching the earth, they enabled astronomers to begin charting X-ray sources in the heavens. Old radar antennas were converted into sensitive radio telescopes, making it possible for scientists to listen to more of the sky's puzzling beeps, squeals and hums. Some of this noise came from so-called radio galaxies that were all but invisible in the mirrors and lenses of ordinary optical telescopes. Other signals came from the distant and powerful quasars. At Bell Telephone Labs, scientists working on a new satellite communications system even "heard" a low-level microwave hiss that may be lingering radiation of the Big Bang.

Optical astronomy also leaped ahead. Aided by the new electronics and computers, the big mirrors could peer into the very heart of galaxies. Some of these islands of stars swirled with turbulence. Others were catapulting jets of matter into space at close to the speed of light. Finally, the space age ushered in the era of unmanned satellites. Now remote-controlled observatories could be permanently posted in orbit. Never before had the heavens been so carefully watched.

The new technology not only opened new windows on the universe, but also raised another possibility: that gravitational collapse might well be the driving force behind these awesome heavenly happenings. Just as scientists were starting to dust off Oppenheimer's old papers, another discovery, largely serendipitous, made the reports more relevant than ever.

In 1967 a young Irish graduate student named Jocelyn Bell, working under Radio Astronomer Anthony Hewish at Cambridge, discovered a series of regularly spaced signals originating far beyond the solar system. At first she and Hewish wondered whether they might be coming from an extraterrestrial civilization trying to communicate with other intelligent beings. The scientists thus called the first such beeping source--and three new ones discovered soon thereafter--LGMS (for Little Green Men). But after the discovery of still more of these objects, it quickly became apparent that the signals--which were dubbed pulsars--came from something perhaps almost as incredible: the long-postulated neutron stars. Spinning rapidly and accelerating particles in their strong magnetic fields, neutron stars apparently acted like celestial lighthouses, giving off beams of radiation that swept the earth during each rotation. Indeed, one such star was soon found flashing on and off 30 times a second in the very heart of the Crab Nebula, just as Zwicky and Baade had predicted 34 years earlier.

That was enough to convince even skeptics that if gravitational collapse could produce objects as densely packed as neutron stars, it might indeed create black holes. Going beyond Chandrasekhar's limit, scientists at Caltech, Cambridge, M.I.T., Harvard, Princeton and elsewhere determined that it would take a mass only about three times that of the sun to crush into oblivion even tightly packed neutrons. There was no shortage of black-hole candidates; astronomers have found innumerable stars big enough to become black holes, some of them so-called supergiants 40 or 50 tunes the mass of the sun.

But while relatively nearby white dwarfs radiate enough light to be photographed through large telescopes, and neutron stars give off revealing beeps, black holes are by their nature singularly, so to speak, uncommunicative. Then how could they ever be identified? Astronomers rose to the challenge. Unlike the solitary sun, many stars are binaries--pairs of stars that travel close together through space locked in a gravitational embrace and orbiting a common center of gravity. If one massive star in a binary system were to suffer gravitational collapse and form a black hole, scientists reasoned, it would continue to exert gravitational pull on its still visible companion. In fact, that is just what seems to be happening, some 6,000 light-years away, in the constellation Cygnus. Exerting its gravitational attraction on its huge visible neighbor, the black hole apparently stretches the star into an egg shape and pulls off large amounts of gases. As the particles of gas spiral inward, or biting the black hole in ever tighter circles before entering the event horizon, they collide, compress and heat up. Temperatures within this so-called accretion disk of gases surrounding the black hole reach 10 million degrees C, sending streams of intense X rays into space.

It is this telltale radiation that was apparently detected from Cygnus by the pioneering Uhuru and Copernicus X-ray satellites. A similar partnership of two stars--one of them also a black hole--may be responsible for the X rays that are being picked up from Scorpius.

Scientists also have other schemes for "finding" black holes.

According to general relativity, such violent activity as stellar collapse and the collision of certain types of black holes should release gravity waves. These waves are to the gravitational force what light and radio waves are to the electromagnetic force.

But because gravity is so weak at long range, detecting its waves, says Harvard's Smarr, is "like measuring fluctuations in the dis tance between the earth and sun equal to the diameter of a human hair." So far no one has been able to accomplish that feat. But investigators in the U.S. and abroad are hoping to succeed with a new generation of extremely sensitive gravity detectors that rely on lasers, devices using superchilled metals and other advanced gadgetry.

Scientists are also looking to other new instruments to prove the case for black holes. Among them:

P: Improved "high-energy" astronomical satellites. These would be sensitive enough to pick up gamma radiation from Hawking's mini-black holes.

P: The so-called Very Large Array, a monstrous 48 km by 32 km (30 miles by 20 miles) Y-shaped radio telescope, consisting of 27 individual dish-shaped antennas, that is now about half completed in New Mexico. It is designed to probe deep into distant quasars, which may be powered by black holes.

P: The Space Telescope, a 2.4 m (94 in.) mirror scheduled to be placed in orbit by the space shuttle in the early 1980s. Flying above the obscuring atmosphere, this observatory should pick up a variety of celestial phenomena, including infrared and ultraviolet radiation, and reveal hidden structural details of galaxies that may harbor black holes.

If these instruments find strong evidence of a black hole, how significant would that discovery be? For one thing, proof of the existence of black holes would clear away some of the mystery about both the evolution and the fate of the universe. Scientists generally agree that the universe is expanding, that its galaxies are still rushing outward from the original Big Bang. But they are uncertain about whether the expansion will continue forever. True, gravitational attraction among the galaxies is slowing the outward rush, but unless there is sufficient mass in the universe, the expansion will never completely halt.

Astronomers so far have been unable to find the necessary mass in the observable galaxies and gas clouds, but if black holes do exist in the numbers that some scientists believe, they would provide additional gravitational braking and reverse the expansion. If that is the case, the universe--like a giant, collapsing star will eventually begin falling back upon itself. Some 50 billion years from now, the galaxies will crush together to form the ultimate singularity--a single gigantic black hole--and the universe will cease to exist. Wheeler, for one, sees no escape from what he calls "this final crunch." Says he:

"This universe is our only chance, and we had best make the most of it."

But what about the near future, and now? Could black holes have any effect on contemporary civilization? Says the University of Arizona's Roger Angel: "There is no practical use for these things." Well, perhaps for the moment. But even normally cautious scientists like to dream, and nothing seems to evoke futuristic reveries as much as black holes.

At a 1974 scientific meeting in Manhattan, Lowell Wood, a young physicist from California's Lawrence Livermore Laboratory, delighted his colleagues (although he did not exactly convince them) with a plan to give the earth a virtually limitless energy supply. He suggested tapping the energy of a mini-black hole in orbit around the planet. From a spacecraft orbiting at a safe distance, pellets would be fired at the hole. This would create so much heat that the energy could be converted into microwaves and beamed down to earth. Even Wheeler, who is now at the University of Texas, and his former student, Kip Thorne, once proposed construction of an entire civilization around a black hole (just outside the event horizon, of course).

The purpose of such technological derring-do? To create the ultimate garbage dump. Because of the strange physics at the black hole's boundary zone, waste material dropped toward it would only be partially consumed; some of the material would be flung back out at much greater speed. This material could be caught and its extra energy harnessed, like rushing water, to power the civilization. The only hitch: the engineers would have to be careful not to "feed" the black hole too much garbage, lest its event horizon expand and swallow up the whole civilization.

No one can say if anything like these visionary schemes will ever be possible. Indeed, for all the enthusiasm about black holes, some doubts about their very existence linger. But the current intellectual ferment about them transcends the importance of both their reality and practicality. Just by thinking on such a grand scale, humanity not only enlarges its universe but expands and ennobles itself. Perhaps the ideal metaphor is not Piglet's Heffalump but Browning's famous declamation: "Ah, but a man's reach should exceed his grasp,/ Or what's a heaven for." To the growing fraternity of black-hole theorists, that cosmic vision is the ultimate lodestar.

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