Although perhaps best treated in the context of stars in the next STELLAR EPOCH, the most massive black holes likely arose in the GALACTIC EPOCH, roughly a billion years after the Matter Era began. Observations during the 1990s imply that black holes reside in the hearts of most galaxies—relative dormant holes at the cores of normal galaxies and extremely energetic ones powering the active galaxies. So, rather than sidestepping this important issue—a central topic in much of astrophysics today—let’s consider the phenomenon of black holes now.
A black hole is a region containing a huge amount of mass spread throughout a relatively small volume. It’s not an object per se so much as a hole, and one that’s dark to boot. Such a hole still exerts gravity, to be sure exceptionally strong gravity great enough to warp spacetime severely in its vicinity. Its two main features—large mass and small size—guarantee an enormously strong gravitational force. Why? Because one-half of the law of gravity is directly proportional to the mass. The other half dictates that gravity is inversely proportional to the square of the distance over which the mass is spread—the inverse-square law again, as noted in the PARTICLE EPOCH. And because the distance term is squared, the gravitational force greatly intensifies when distances separating any two parts of an object decrease, which is exactly what happens for a compressed object like a black hole.
Gravitational theory—either Newton’s or Einstein’s, they both make this prediction—stipulates that when any object having a mass of ~3 times that of the Sun is no longer countered by any countervailing agent (such as heat in a star, or rotation in a cloud), that object will collapse indefinitely, crushing matter to the dimensions of a point. It implodes catastrophically without limit; apparently nothing can stop it.
Can anyone possibly grasp such a seemingly ridiculous phenomenon? How can an entire star (or larger) shrink to the size of an atom (or smaller), while presumably on its way to infinitely small dimensions? Does this make any sense? Well, detailed mathematical studies do predict that, without some agent to compete against gravity, massive objects are expected to instantaneously shrink to singular points of infinitesimal volume—a singularity, much as posed in the PARTICLE EPOCH for the origin of the Universe—which is why some researchers consider black holes as “laboratories” in which to explore aspects of the big bang itself. Strange as these statements may seem, observational evidence mounts daily in good agreement with theory. Black holes apparently really do exist.
Properties of Black Holes Though the messy mathematics needed to understand black holes intimately are beyond the scope of this Web site, we can still explore a few qualitative aspects of these extremely dense and bizarre regions of spacetime. The details are sketchy, precisely because the behavior of matter at extreme densities is not well understood. The phenomena of magnetism and rotation are also hard to model for highly compressed objects; the laws of physics here are clearly incomplete. Whoever manages to decipher the details of this tricky subject, called "magnetohydrodynamics," will surely become famous.
Consider first the concept of escape velocity—the speed needed for one object to escape from the gravitational pull of another. For any relatively small piece of matter—a molecule, baseball, rocket, whatever—that velocity is proportional to the square root of an object’s mass divided by its radius:
escape velocity α (mass of object / radius of object)1/2 .
For example, on Earth, with a radius of ~6400 km (or ~4000 miles), the escape velocity equals ~11 km/s (or ~25,000 mph). To launch anything away from the surface of our planet, it must have a velocity greater than this, explaining why typical speeding bullets, fired at ~2 km/s, return to Earth’s surface. Also, the International Space Station, for example, orbits Earth at a speed of ~8 km/s, but the interplanetary probes, such as Voyager that bypassed Jupiter or Viking that landed on Mars, required a boost to 11 km/s to physically escape Earth’s gravitational pull.
Consider now a hypothetical experiment for which the apparatus is a gigantic, 3-dimensional vise (Figure 2.6). Imagine the vise to be large enough to hold the entire Earth and, as awful as it sounds, for Earth to be squeezed on all sides. As our planet shrinks under the assault, its density rises because the total amount of mass remains constant inside an ever-shrinking volume. Accordingly, the escape velocity increases.
Suppose that our planet is compressed to ¼ its present size, thus doubling the escape velocity. Anything attempting to escape from this hypothetically compressed Earth would then need a velocity of at least 22 km/s. Imagine compressing Earth still more. Squeeze it, for example, by an additional factor of 1000, making its radius hardly more than a kilometer. Now its escape velocity increases dramatically, to many hundred kilometers per second.
And so it goes: As an object of any mass contracts, the gravitational force grows stronger at its surface, mostly because of increased density. In fact, if this frightful vise were to compact our home planet hard enough to crush it to merely a centimeter across (about half an inch), then the escape velocity would reach 300,000 km/s (or 186,000 miles/second). And this is no ordinary velocity; it’s the velocity of light, the fastest velocity allowed by the laws of physics as we now know them.
So if, by some fantastic means, the entire planet Earth could be shrunk to the size of a pea, then its escape velocity would have to exceed the velocity of light. And since that’s impossible, the compelling conclusion is that nothing—absolutely nothing—could get away from the surface of such a compressed “Earth.” There is simply no way to launch away a rocket, a beam of light, or anything whatsoever. Furthermore, no exchange of information would be permitted with such an astronomical object. It would have become invisible and uncommunicative, making all too clear the origin of the term “black hole.” For all practical purposes, such an ultra-compact object disappears from the Universe!
The above example is of course hypothetical. It’s likely (and fortunate) that no such cosmic vise exists capable of squeezing the entire Earth to centimeter dimensions. But in massive stars and galaxies, such a vise does in fact exist—the force of gravity. The relentless pull of gravity is truly strong enough to compress dead stars and galaxy cores to extraordinarily small dimensions. A fearsome gravitational force in massively compact objects is not at all hypothetical; it’s real.
Gravity cannot crush Earth in this way because our planet simply lacks enough mass. The collective gravitational pull of every part of Earth on all other parts of Earth is not powerful enough to compact it more than it is already. However, as we shall see in the next STELLAR EPOCH, when the nuclear fires have ceased at the end of a star’s life, gravity can literally crush a more massive star on all sides, thereby packing a vast amount of matter into a very small sphere.
When stars have more than several solar masses, the critical size at which the escape velocity equals that of light is not, as for Earth, of centimeter dimensions. For typically massive stellar core remnants, this critical size is comparable to kilometers. For example, a 10-solar-mass star would have a critical size of about 30 km. This critical size below which astronomical objects are predicted to vanish is given a special name. Astronomers call it the “event horizon,” a region within which no event can ever be seen, heard, or known by anyone outside. Accordingly, the event horizons of Earth and of a 10-solar-mass star equal 1 cm and 30 km, respectively.
We might then claim that magicians really could make coins and rabbits disappear provided they squeezed their hands hard enough. Even people could disappear if compressed to a size smaller than 10-23 cm! In English units, that’s a trillionth of a trillionth of an inch. Gravity won’t naturally do it to us, though, again because we are just too puny. The collective gravitational pull of all the atoms in our bodies falls far short of the force needed to compact us to this minuscule size. Nor does any technological device presently known come close to doing so.
The important point here is the following: Should no force, or counteracting agent of some sort, be capable of withstanding the self-gravity of a celestial object having several solar masses or more, then such a hefty hulk will naturally collapse of its own accord to an ever-diminishing size. Theory demands that the infall of such a massive object will not even stop at its event horizon. An event horizon is not a physical boundary of any type, just a communications barrier. The massive object shrinks right on past it to smaller sizes, presumably on its way toward becoming an infinitely small point—that singularity again. We say “presumably” because physicists are unsure if any undiscovered forces can halt the catastrophic collapse somewhere between the event horizon and the point of singularity. This, again, is the realm of the as-yet-conceived subject of quantum gravity, the holy grail of the previous PARTICLE EPOCH.
Warping Spacetime Black holes are products largely of Einstein’s relativity theory, although a logical extrapolation of Newton’s law of gravity does permit their existence. Whereas the Newtonian theory of gravity describes many other odd phenomena in the Universe, only the Einsteinian theory of spacetime can properly account for the truly bizarre properties of black holes where matter becomes extraordinarily dense. Of particular interest, and to make a connection with the spacetime concepts of the PARTICLE EPOCH, the mass contained within a black hole is expected to warp greatly both space and time in its vicinity. Close to the hole, the gravitational force becomes overwhelming and the curvature of spacetime extreme. At the event horizon itself, the curvature is so severe that spacetime folds over onto itself, causing objects within it to become trapped and disappear.
Several props can help us visualize the curvature of spacetime near a black hole. Each way is, however, only an analogy. The problem here, as earlier in the case of the whole Universe, is our inability to deal conceptually with four dimensions. Here’s one such fanciful analogy designed to elucidate the formation of black holes and the spacetime warp caused by them:
Imagine a large group of people living on an enormous rubber sheet—a gigantic trampoline of sorts, as sketched in Figure 2.7. Deciding to hold a reunion, all except one person converge on a given location at a given time. Their reunion is to be an event in spacetime. The one person remaining behind can still keep in touch by means of “message balls” rolled out to him along the rubber sheet. These balls are the analogue of radiation traveling at the velocity of light, while the rubber sheet mimics the fabric of spacetime itself.
As the people converge at the appointed spot (marked by an X in the figure), the rubber sheet sags under their growing weight. Their accumulating mass in such a small place creates an increasingly large spacetime curvature. The message balls can still reach the lone person residing far away in nearly flat spacetime, but they arrive less frequently as the sheet becomes progressively more warped.
Finally, when enough people have gathered at the appointed spot, their mass becomes too great for the rubber to support. The sheet breaks and compresses them into a bubble, sending them into oblivion while severing communications with the lone survivor outside. Regardless of the speed of the last message ball, it cannot quite outrun the downward-stretching sheet.
Analogously, a black hole is theorized to warp spacetime completely around on itself, thereby isolating it from the rest of the Universe.
Caution Two important caveats pertain to black holes. The first is that they’re not cosmic vacuum cleaners; they don’t cruise around interstellar space, sucking up everything in sight. The movements of objects near black holes mimic those of any object near a region of concentrated mass. The only difference is that, in the case of a black hole, objects skirt or orbit about a dark, invisible region, where nothing at all can be seen. Neither emitted nor reflected radiation of any sort emanates from the position of the black hole itself.
Black holes, then, don’t go out of their way to drag in matter, but if some matter does happen to infall via the normal pull of gravity, it will be unable to get out. Black holes are like turnstiles, permitting matter to flow in only one direction—inward. Swallowing matter, they constantly increase their mass as well as their event horizons, for the region of invisibility also depends on the amount of mass trapped inside. Those black holes that really do exist in space are probably enlarging their mass and size, some more than others, all of them apparently gulping, eating, growing....
A whirlpool is an apt analogy for the grip that black holes have on matter. Whirlpools of water, for example, tend to have attractive affects on nearby fish (or trash in a polluted stream). Since the speed of the water is greater closer to the center of the whirlpool, fish entering an area where the water speed is faster than the fish can swim will be sucked inward. Those closest in will never make it out.
Another notable phenomenon of black holes is that their strong gravity causes great tidal stress. An unfortunate person, falling feet first into a black hole, would find himself stretched enormously in height, all the while being squeezed laterally. He would, moreover, be literally torn apart, for the pull of gravity would be stronger at his feet than at his head. He wouldn’t stay in one piece for more than a fraction of a second after passing the event horizon. Similar distortion and breakup apply to any kind of matter near a black hole. Whatever falls in—gas, people, robots, whatever—is vertically stretched and horizontally compressed in the process of being accelerated to high speeds. The upshot is numerous and violent collisions among the torn-up debris, causing much heating of the matter just before plunging into the hole.
The destructive effect of tides and collisions is so efficient that, prior to submersion below the hole’s event horizon, matter outside a black hole can be effectively converted to heat energy while falling inward. Although radiation ceases to be detectable once the hot matter dips below the event horizon, regions just outside black holes are expected to be energetically emitting radiation, mostly in the x-ray part of the spectrum since the matter is so hot. There is nothing exotic about this emission; such a thermal process occurs solely owing to heated gas. Contrary to popular belief, however, black holes can then appear to distant observers as bright points of radiation and prodigious sources of energy.
With this in mind and being only partly facetious, perhaps black-hole research may eventually result in practical applications after all. Through some marvel of technology, our descendants might someday learn how to compact garbage to a minute size—after which it would disappear! Not only that, the crushed garbage would emit copious amounts of energy in return. Maybe black holes are just what the doctor ordered for a technological civilization (like ours) long on pollution and short on energy. An ability to tap this energy safely may be a major milestone in the history of any long-lived civilization.
Inside Black Holes Of much interest is the obvious question, What lies within the event horizon of a black hole? What’s it like deep inside? The answers are simple: No one knows.
Some researchers maintain that the inner workings of black holes are irrelevant. In situ observations could conceivably be done by robots sent “down under” to test the nature of space and time beneath the event horizon, but that information could never reach the rest of us outside. Apparently, no theory offered to explain the hidden recesses of black holes could ever be put to the experimental test. Anyone’s guess seems as valid as anyone else’s. Perhaps the inner sanctums of black holes then represent the ultimate in the unknowable. For that very reason, though, other researchers argue that it’s of utmost importance to unravel the nature of black holes, lest we someday begin to worship them. Sounds ridiculous, but whole segments of humankind have often revered the unknowable, venerating that which cannot be tested experimentally. Come to think of it, many still do in 21st-century society.
What sense are we to make of black holes? The basis for these outlandish objects is the relativistic concept that mass curves spacetime—an admittedly weird phenomenon, yet one that has been partially tested locally in our Solar System. The larger the mass concentration, the greater the warp, and thus the stranger the observational consequences. Perhaps. Some theorists are convinced that relativity is incorrect, or at least incomplete, when applied to black holes. It does seem nonsensical to claim that very massive astronomical objects will collapse catastrophically to infinitely small points. Not even our wildest imaginations can visualize such phenomena; science-fiction stories fall short, mathematicians are baffled. Maybe the current laws of physics are inadequate in the vicinity of a singularity; precisely at the point of singularity, general relativity is probably absurd. On the other hand, perhaps matter trapped in black holes never does compress all the way down to that mathematically arcane singularity. Perhaps matter just approaches this bizarrest state in all of science, in which case relativity theory may still hold true.
This is where in many accounts, even those held by leading scientists, writers often launch into discussions of parallel universes, multiple universes, hyperspace, warp drive, worm holes, time travel, other dimensions, and a host of other “possibilities,” both remote and fanciful. But these and other like-minded speculations are not within the scope of this Web site. Here, we strive to stay on reasonably solid, empirical ground, appealing to tested (or at least testable) ideas and acquired data, while admitting our ignorance wherever it lay. And when it comes to the secluded sanctorum of black holes, the honest answer is that scientists just don’t know what to make of them—nor will we likely ever learn much until the frontier subject of quantum gravity is realized and mastered.
Observational Evidence Despite their incredulity, black holes seemingly do exist. In addition to the “smallish,” stellar black-hole candidates best assessed in the next STELLAR EPOCH, many astronomers contend that the much larger galaxies display convincing evidence for black-holes. Particularly intriguing are the centers of galaxies, including the core of our own Milky Way, ~26,000 light-years from Earth. Our Galaxy’s midsection should provide us with a stunning view, given that it’s teeming with so many billions of densely packed stars. But we don’t see its brilliance because its midst is completely obscured by dust, denying studies with optical telescopes; even the largest such devices can visually see only about a tenth of the way toward the galactic center. Fortunately, longer-wavelength, radio and infrared observations are possible, enabling us to probe more deeply into the heart of the Galaxy (much like radar cuts through thick fog on Earth). And what was found in the innermost few hundred light-years initially yielded spectacularly unexpected results; now, in retrospect a few decades later, the findings seem typical of the black holes probably lurking in the hearts of galaxies everywhere.
At the Milky Way’s core, infrared sensing reveals thousands of stars swarming per cubic light year—a stellar density more than a million times greater than in our solar neighborhood. Giant nebulae tens of light-years across, rich in gas and embedded among even bigger clouds loaded with dust, reside in a ring-like structure more than 1000 light-years across, the whole formation housing some tens of thousands of solar masses and rotating at a fast clip of ~100 km/s (or >200,000 miles/hr). And in the center of the ring is an intense radio source—the dynamical nucleus of our Galaxy.
On even smaller scales, high-resolution radio maps show an inner ring of gas less than 10 light-yeas across, rotating even more rapidly (>1000 km/s) and resembling a colossal whirlpool at the very heart of our Galaxy. This remarkable realm, quite unlike anything near Earth, has been closely monitored ever since it was first found some 30 years ago, including recent outbursts at x-ray wavelengths implying the presence of a spinning, white-hot accretion disk of 106 K gas right in the middle of it all. Magical and mysterious, yet not mystical, the enshrouded nature of this most perplexing piece of galactic real estate so far and foreign is slowly being deciphered.
Frustrated late one evening at the Harvard Observatory, a few scientists wandered to Cambridge Common where we perched ourselves on a bench near the edge of the park. Straining to fathom the locations of crosswalks, benches and trees, we gained some insight into the problem of trying to map the Milky Way while stuck inside it. Barring ourselves from walking, bicycling, or otherwise sauntering about, we soon discovered that charting the park’s layout is no easy task. Any resulting map would likely be subject to distortion, obscuration, and incompleteness. Statues and signposts—and especially the grand monument near the common’s center—seemed especially strange and intriguing from a distance, for they resembled none of the familiar shrubs and benches near the outer part of the park. And so it is with our Milky Way Galaxy. Relegated perhaps forever to the galactic boondocks, we strain to unravel the spread of stars, gas, and dust in that part of the Universe we call home.
Models capable of accounting for most of the galactic-center observations to date stipulate (see Figure 2.8) that a rapidly rotating halo of thin, hot, ionized matter surrounds a furiously spinning vortex of even hotter, denser matter. This swirling mess of stars, gas, and dust is apparently orbiting—and here’s the punch line—a tremendously compact object housing ~4x106 solar masses, all packed into a region comparable to our Solar System. Such an enormously massive and compact blob is needed to give the maelstrom some structural integrity—to prevent the whirlpool of gas from dispersing into the outer regions of the Galaxy. Fast rotations doubtless produce strong centrifugal forces and, unless a huge mass gravitationally pulls back, the gas would be flung away like mud from the edge of a spinning bicycle wheel. The implication that millions of stars are compressed to planetary-system dimensions follows from simple, well-understood physics, even if the result borders on Surrealism.
Though the details are controversial, a consensus now seems at hand that a supermassive, ultracompact “something” resides at the hub of our Milky Way Galaxy. As best we can tell, that something can be only one thing—a black hole in space. Not to worry, the hole currently seems rather quiescent, if not dormant, and in any case is more than two billion times farther from Earth than is the Sun.
Our Milky Way isn’t alone in having a troublesome core. Recent observations, such as those in Figure 2.9, imply the presence of supermassive objects in or near the middle of many other galaxies. The evidence here is much the same as for our own Galaxy, with gas and stars in the innermost regions of several normal galaxies, including perhaps nearby Andromeda, observed to be rapidly whirling—apparently, again, centered on black holes of millions of solar masses. And although the active galaxies cannot be seen as well owing to their greater distances, observations of them also suggest that highly compact regions lurk in their hearts, usually housing even more gyrating matter than at the cores of the normal galaxies. Astonishingly, for some of the most active galaxies, several billion—not million, but billion—solar masses are inferred, all within a region less than a few light-years across. Perhaps these central whirlpools are remnants of the primordial eddies that gave rise to the galaxies, as noted below.
Astronomers now sense that the center of virtually every galaxy is inhabited by a supermassive black hole. Normal galaxies such as our own probably have relatively small holes of “mere” millions of solar masses, most of them, as for our Galaxy, now relatively inactive for lack of fuel. Those galaxies considered more active have larger black holes, often on the order of billions of solar masses, as betrayed by their more intense radiation. It is their enhanced emission of energy that makes them “active,” largely because we see many of the distant, active galaxies in their youth when fuel was more plentiful.
As bizarre as this scenario seemed when first proposed in the 1980s, astrophysicists now generally agree that the great energetics of the active galaxies are naturally explained by matter perishing within the clutches of supermassive black holes. Thus, we discern one of the greatest paradoxes in science, as forewarned earlier in this section: Black holes trigger some of the brightest objects in the Universe—all of it caused by matter being gobbled, distorted, accelerated, and heated before disappearing below their event horizons. How the enigmatic jets perpendicular to a black hole’s accretion disk manage to eject matter despite the powerful gravity of the hole, however, remains a considerable puzzle.
Not inconceivably, the most energetic objects in the Universe—the innocuous-looking yet powerful quasars—might be ruled by hypermassive black holes that regularly consume whole stars. Roughly 10 stars devoured per year would do it for typical quasars; ~1000 stars per year, or therefore a few per day, would be needed to explain the brightest of them. If so, then black holes in quasars might be even more massive, more compact, and more abnormal than the billion-solar-mass objects implied for the active galaxies. This idea, however hard to swallow intellectually, since it’s so foreign compared to the more mundane events near us in space and time, can seemingly explain most quasar observations. It also has the added advantage of resembling the process thought to power smaller-scale yet still violent regions, such as normal galactic centers and stellar x-ray sources within galaxies, implying that unifying principles may be at work on many scales in Nature.
Clearly, a complete understanding of the powerhouse galaxies lies partly buried deep in their cores, awaiting future explorers to discover, unravel, and share their secrets. There, their central engines are both the instigators of change and the recipients of change; again akin to biological events broadly considered, black holes drive change and adapt to it. Yet the timescales for noticeable change differ so markedly—in biology on the order of thousands to millions of years for species change, in astronomy easily millions to billions of years for architectural change. Astrophysicists are still learning to decipher the clues hidden within invisible radiation emitted by alien environments near hugely massive and totally invisible black holes. We are only beginning to appreciate the full magnitude of these strange new realms deep in the hearts of galaxies.
More Caution Some final words of caution regarding black holes, large and small: Forces may yet be discovered capable of withstanding the relentless pull of gravity, even that near exceedingly massive and compact astronomical objects. Magnetism and rotation have not yet been fully incorporated into black-hole theory, and no one knows what to expect regarding the behavior of gravity on deeply submicroscopic, quantum scales. Massive clusters of dark stars and ultradense pools of elementary particles have been proposed as alternatives to black holes, as have queer and inventive groupings of more exotic kinds of dark matter. That these are all terribly hard problems to solve is an understatement, so much so that some of the best minds confess ignorance as to how to go about even attacking them. Serious research regarding realistic models of black holes is only beginning at many observatories around the world.
Skepticism is healthy in science. Unless astrophysicists can find direct, or compellingly indirect, evidence for the existence of black holes, neither of which is currently at hand, then the whole concept of black holes may well turn out to be no more than a whim of human fantasy—another case of mathematics gone awry without the check and balance of tested physical law. The nature of matter, energy, space, and time deep down inside event horizons may be no more significant than a challenging and amusing academic problem devoid of reality.
On the other hand, the Universe did emerge from what seems to have been a naked singularity ~14 billion years ago. Of all the amassments now known or suspected to be part of our cosmic inventory, black-hole singularities might just be the keys needed to unlock an understanding of the (yes, mystical) creation state from which the Universe arose. By theoretically studying the nature of black holes, and especially by observationally probing their physical behavior, we shall perhaps someday be in a better position to address the most fundamental problem of all—the origin of the Universe itself.