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CHAPTER 6 BLACK HOLES
The term black hole is of very recent origin. It was coinedin 1969 by the American scientist John Wheeler as a graphicdescription of an idea that goes back at least two hundredyears, to a time when there were two theories about light: one,which Newton favored, was that it was composed of particles;the other was that it was made of waves. We now know thatreally both theories are correct. By the wave/particle duality ofquantum mechanics, light can be regarded as both a wave anda particle. Under the theory that light is made up of waves, itwas not clear how it would respond to gravity. But if light iscomposed of particles, one might expect them to be affected bygravity in the same way that cannonballs, rockets, and planetsare. At first people thought that particles of light traveledinfinitely fast, so gravity would not have been able to slow themdown, but the discovery by Roemer that light travels at a finitespeed meant that gravity might have an important effect.
On this assumption, a Cambridge don, John Michell, wrote apaper in 1783 in the Philosophical Transactions of the RoyalSociety of London in which he pointed out that a star that wassufficiently massive and compact would have such a stronggravitational field that light could not escape: any light emittedfrom the surface of the star would be dragged back by thestar’s gravitational attraction before it could get very far. Michellsuggested that there might be a large number of stars like this.
Although we would not be able to see them because the lightfrom them would not reach us, we would still feel theirgravitational attraction. Such objects are what we now call blackholes, because that is what they are: black voids in space. Asimilar suggestion was made a few years later by the Frenchscientist the Marquis de Laplace, apparently independently ofMichell. Interestingly enough, Laplace included it in only the firstand second editions of his book The System of the World, andleft it out of later editions; perhaps he decided that it was acrazy idea. (Also, the particle theory of light went out of favorduring the nineteenth century; it seemed that everything couldbe explained by the wave theory, and according to the wavetheory, it was not clear that light would be affected by gravityat all.)In fact, it is not really consistent to treat light likecannonballs in Newton’s theory of gravity because the speed oflight is fixed. (A cannonball fired upward from the earth will beslowed down by gravity and will eventually stop and fall back;a photon, however, must continue upward at a constant speed.
How then can Newtonian grav-ity affect light?) A consistenttheory of how gravity affects light did not come along untilEinstein proposed general relativity in 1915. And even then itwas a long time before the implications of the theory formassive stars were understood.
To understand how a black hole might be formed, we firstneed an understanding of the life cycle of a star. A star isformed when a large amount of gas (mostly hydrogen) startsto collapse in on itself due to its gravitational attraction. As itcontracts, the atoms of the gas collide with each other moreand more frequently and at greater and greater speeds - thegas heats up. Eventually, the gas will be so hot that when thehydrogen atoms collide they no longer bounce off each other,but instead coalesce to form helium. The heat released in thisreaction, which is like a controlled hydrogen bomb explosion, iswhat makes the star shine. This additional heat also increasesthe pressure of the gas until it is sufficient to balance thegravitational attraction, and the gas stops contracting. It is a bitlike a balloon - there is a balance between the pressure of theair inside, which is trying to make the balloon expand, and thetension in the rubber, which is trying to make the balloonsmaller. Stars will remain stable like this for a long time, withheat from the nuclear reactions balancing the gravitationalattraction. Eventually, however, the star will run out of itshydrogen and other nuclear fuels. Paradoxically, the more fuel astar starts off with, the sooner it runs out. This is because themore massive the star is, the hotter it needs to be to balanceits gravitational attraction. And the hotter it is, the faster it willuse up its fuel. Our sun has probably got enough fuel foranother five thousand million years or so, but more massivestars can use up their fuel in as little as one hundred millionyears, much less than the age of the universe. When a starruns out of fuel, it starts to cool off and so to contract. Whatmight happen to it then was first understood only at the endof the 1920s.
In 1928 an Indian graduate student, SubrahmanyanChandrasekhar, set sail for England to study at Cambridge withthe British astronomer Sir Arthur Eddington, an expert ongeneral relativity. (According to some accounts, a journalist toldEddington in the early 1920s that he had heard there wereonly three people in the world who understood generalrelativity. Eddington paused, then replied, “I am trying to thinkwho the third person is.”) During his voyage from India,Chandrasekhar worked out how big a star could be and stillsupport itself against its own gravity after it had used up all itsfuel. The idea was this: when the star becomes small, thematter particles get very near each other, and so according tothe Pauli exclusion principle, they must have very differentvelocities. This makes them move away from each other andso tends to make the star expand. A star can thereforemaintain itself at a constant radius by a balance between theattraction of gravity and the repulsion that arises from theexclusion principle, just as earlier in its life gravity was balancedby the heat.
Chandrasekhar realized, however, that there is a limit to therepulsion that the exclusion principle can provide. The theory ofrelativity limits the maximum difference in the velocities of thematter particles in the star to the speed of light. This meansthat when the star got sufficiently dense, the repulsion causedby the exclusion principle would be less than the attraction ofgravity. Chandrasekhar calculated that a cold star of more thanabout one and a half times the mass of the sun would not beable to support itself against its own gravity. (This mass is nowknown as the Chandrasekhar limit.) A similar discovery wasmade about the same time by the Russian scientist LevDavidovich Landau.
This had serious implications for the ultimate fate of massivestars. If a star’s mass is less than the Chandrasekhar limit, itcan eventually stop contracting and settle down to a possiblefinal state as a “white dwarf” with a radius of a few thousandmiles and a density of hundreds of tons per cubic inch. Awhite dwarf is supported by the exclusion principle repulsionbetween the electrons in its matter. We observe a largenumber of these white dwarf stars. One of the first to bediscovered is a star that is orbiting around Sirius, the brighteststar in the night sky.
Landau pointed out that there was another possible finalstate for a star, also with a limiting mass of about one or twotimes the mass of the sun but much smaller even than a whitedwarf. These stars would be supported by the exclusionprinciple repulsion between neutrons and protons, rather thanbetween electrons. They were therefore called neutron stars.
They would have a radius of only ten miles or so and adensity of hundreds of millions of tons per cubic inch. At thetime they were first predicted, there was no way that neutronstars could be observed. They were not actually detected untilmuch later.
Stars with masses above the Chandrasekhar limit, on theother hand, have a big problem when they come to the end oftheir fuel. In some cases they may explode or manage tothrow off enough matter to reduce their mass below the limitand so avoid catastrophic gravitational collapse, but it wasdifficult to believe that this always happened, no matter how bigthe star. How would it know that it had to lose weight? Andeven if every star managed to lose enough mass to avoidcollapse, what would happen if you added more mass to awhite dwarf ‘or neutron star to take it over the limit? Would itcollapse to infinite density? Eddington was shocked by thatimplication, and he refused to believe Chandrasekhar’s result.
Eddington thought it was simply not possible that a star couldcollapse to a point. This was the view of most scientists:
Einstein himself wrote a paper in which he claimed that starswould not shrink to zero size. The hostility of other scientists,particularly Eddington, his former teacher and the leadingauthority on the structure of stars, persuaded Chandrasekhar toabandon this line of work and turn instead to other problemsin astronomy, such as the motion of star clusters. However,when he was awarded the Nobel Prize in 1983, it was, at leastin part, for his early work on the limiting mass of cold stars.
Chandrasekhar had shown that the exclusion principle couldnot halt the collapse of a star more massive than theChandrasekhar limit, but the problem of understanding whatwould happen to such a star, according to general relativity,was first solved by a young American, Robert Oppenheimer, in1939. His result, however, suggested that there would be noobservational consequences that could be detected by thetelescopes of the day. Then World War II intervened andOppenheimer himself became closely involved in the atom bombproject. After the war the problem of gravitational collapse waslargely forgotten as most scientists became caught up in whathappens on the scale of the atom and its nucleus. In the1960s, however, interest in the large-scale problems ofastronomy and cosmology was revived by a great increase inthe number and range of astronomical observations broughtabout by the application of modern technology. Oppenheimer’swork was then rediscovered and extended by a number ofpeople.
The picture that we now have from Oppenheimer’s work isas follows. The gravitational field of the star changes the pathsof light rays in space-time from what they would have beenhad the star not been present. The light cones, which indicatethe paths followed in space and time by flashes of light emittedfrom their tips, are bent slightly inward near the surface of thestar. This can be seen in the bending of light from distantstars observed during an eclipse of the sun. As the starcontracts, the gravitational field at its surface gets stronger andthe light cones get bent inward more. This makes it moredifficult for light from the star to escape, and the light appearsdimmer and redder to an observer at a distance. Eventually,when the star has shrunk to a certain critical radius, thegravitational field at the surface becomes so strong that thelight cones are bent inward so much that light can no longerescape (Fig. 6.1). According to the theory of relativity, nothingcan travel faster than light. Thus if light cannot escape, neithercan anything else; everything is dragged back by thegravitational field. So one has a set of events, a region ofspace-time, from which it is not possible to escape to reach adistant observer. This region is what we now call a black hole.
Its boundary is called the event horizon and it coincides withthe paths of light rays that just fail to escape from the blackhole.
In order to understand what you would see if you werewatching a star collapse to form a black hole, one has toremember that in the theory of relativity there is no absolutetime. Each observer has his own measure of time. The time forsomeone on a star will be different from that for someone at adistance, because of the gravitational field of the star. Supposean intrepid astronaut on the surface of the collapsing star,collapsing inward with it, sent a signal every second, accordingto his watch, to his spaceship orbiting about the star. At sometime on his watch, say 11:00, the star would shrink below thecritical radius at which the gravitational field becomes so strongnothing can escape, and his signals would no longer reach thespaceship. As 11:00 approached his companions watching fromthe spaceship would find the intervals between successive signalsfrom the astronaut getting longer and longer, but this effectwould be very small before 10:59:59. They would have to waitonly very slightly more than a second between the astronaut’s10:59:58 signal and the one that he sent when his watch read10:59:59, but they would have to wait forever for the 11:00signal. The light waves emitted from the surface of the starbetween 10:59:59 and 11:00, by the astronaut’s watch, wouldbe spread out over an infinite period of time, as seen from thespaceship. The time interval between the arrival of successivewaves at the spaceship would get longer and longer, so thelight from the star would appear redder and redder and fainterand fainter. Eventually, the star would be so dim that it couldno longer be seen from the spaceship: all that would be leftwould be a black hole in space. The star would, however,continue to exert the same gravitational force on the spaceship,which would continue to orbit the black hole. This scenario isnot entirely realistic, however, because of the following problem.
Gravity gets weaker the farther you are from the star, so thegravitational force on our intrepid astronaut’s feet would alwaysbe greater than the force on his head. This difference in theforces would stretch our astronaut out like spaghetti or tearhim apart before the star had contracted to the critical radiusat which the event horizon formed! However, we believe thatthere are much larger objects in the universe, like the centralregions of galaxies, that can also undergo gravitational collapseto produce black holes; an astronaut on one of these wouldnot be torn apart before the black hole formed. He would not,in fact, feel anything special as he reached the critical radius,and could pass the point of no return without noticing itHowever, within just a few hours, as the region continued tocollapse, the difference in the gravitational forces on his headand his feet would become so strong that again it would tearhim apart.
The work that Roger Penrose and I did between 1965 and1970 showed that, according to general relativity, there must bea singularity of infinite density and space-time curvature withina black hole. This is rather like the big bang at the beginningof time, only it would be an end of time for the collapsingbody and the astronaut. At this singularity the laws of scienceand our ability to predict the future would break down.
However, any observer who remained outside the black holewould not be affected by this failure of predictability, becauseneither light nor any other signal could reach him from thesingularity. This remarkable fact led Roger Penrose to proposethe cosmic censorship hypothesis, which might be paraphrasedas “God abhors a naked singularity.” In other words, thesingularities produced by gravitational collapse occur only inplaces, like black holes, where they are decently hidden fromoutside view by an event horizon. Strictly, this is what is knownas the weak cosmic censorship hypothesis: it protects observerswho remain outside the black hole from the consequences ofthe breakdown of predictability that occurs at the singularity,but it does nothing at all for the poor unfortunate astronautwho falls into the hole.
There are some solutions of the equations of generalrelativity in which it is possible for our astronaut to see anaked singularity: he may be able to avoid hitting thesingularity and instead fall through a “wormhole” and come outin another region of the universe. This would offer greatpossibilities for travel in space and time, but unfortunately itseems that these solutions may all be highly unstable; the leastdisturbance, such as the presence of an astronaut, may changethem so that the astronaut could not see the singularity untilhe hit it and his time came to an end. In other words, thesingularity would always lie in his future and never in his past.
The strong version of the cosmic censorship hypothesis statesthat in a realistic solution, the singularities would always lieeither entirely in the future (like the singularities of gravitationalcollapse) or entirely in the past (like the , big bang). I stronglybelieve in cosmic censorship so I bet Kip Thorne and JohnPreskill of Cal Tech that it would always hold. I lost the bet ona technicality because examples were produced of solutions witha singularity that was visible from a long way away. So I hadto pay up, which according to the terms of the bet meant Ihad to clothe theirnakedness. But I can claim a moral victory. The nakedsingularities were unstable: the least disturbance would causethem either to disappear or to be hidden behind an eventhorizon. So they would not occur in realistic situations.
The event horizon, the boundary of the region of space-timefrom which it is not possible to escape, acts rather like aone-way membrane around the black hole: objects, such asunwary astronauts, can fall through the event horizon into theblack hole, but nothing can ever get out of the black holethrough the event horizon. (Remember that the event horizonis the path in space-time of light that is trying to escape fromthe black hole, and nothing can travel faster than light.) Onecould well say of the event horizon what the poet Dante saidof the entrance to Hell: “All hope abandon, ye who enterhere.” Anything or anyone who falls through the event horizonwill soon reach the region of infinite density and the end oftime.
General relativity predicts that heavy objects that are movingwill cause the emission of gravitational waves, ripples in thecurvature of space that travel at the speed of light. These aresimilar to light waves, which are ripples of the electromagneticfield, but they are much harder to detect. They can beobserved by the very slight change in separation they producebetween neighboring freely moving objects. A number ofdetectors are being built in the United States, Europe, andJapan that will measure displacements of one part in athousand million million million (1 with twenty-one zeros afterit), or less than the nucleus of an atom over a distance of tenmiles.
Like light, gravitational waves carry energy away from theobjects that emit them. One would therefore expect a system ofmassive objects to settle down eventually to a stationary state,because the energy in any movement would be carried awayby the emission of gravitational waves. (It is rather likedropping a cork into water: at first it bobs up and down agreat deal, but as the ripples carry away its energy, iteventually settles down to a stationary state.) For example, themovement of the earth in its orbit round the sun producesgravitational waves. The effect of the energy loss will be tochange the orbit of the earth so that gradually it gets nearerand nearer to the sun, eventually collides with it, and settlesdown to a stationary state. The rate of energy loss in the caseof the earth and the sun is very low - about enough to run asmall electric heater. This means it will take about a thousandmillion million million million years for the earth to run into thesun, so there’s no immediate cause for worry! The change inthe orbit of the earth is too slow to be observed, but thissame effect has been observed over the past few yearsoccurring in the system called PSR 1913 + 16 (PSR stands for“pulsar,” a special type of neutron star that emits regular pulsesof radio waves). This system contains two neutron stars orbitingeach other, and the energy they are losing by the emission ofgravitational waves is causing them to spiral in toward eachother. This confirmation of general relativity won J. H. Taylorand R. A. Hulse the Nobel Prize in 1993. It will take aboutthree hundred million . years for them to collide. Just beforethey do, they will be orbiting so fast that they will emit enoughgravitational waves for detectors like LIGO to pick up.
During the gravitational collapse of a star to form a blackhole, the movements would be much more rapid, so the rateat which energy is carried away would be much higher. Itwould therefore not be too long ‘ before it settled down to astationary state. What would this final stage look like? Onemight suppose that it would depend on all the complex featuresof the star from which it had formed - not only its mass andrate of rotation, but also the different densities of various partsof the star, and the complicated movements of the gases withinthe star. And if black holes were as varied as the objects thatcollapsed to form them, it might be very difficult to make anypredictions about black holes in general.
In 1967, however, the study of black holes was revolutionizedby Werner Israel, a Canadian scientist (who was born in Berlin,brought up in South Africa, and took his doctoral degree inIreland). Israel showed that, according to general relativity,non-rotating black holes must be very simple; they wereperfectly spherical, their size depended only on their mass, andany two such black holes with the same mass were identical.
They could, in fact, be described by a particular solution ofEinstein’s equations that had been known since 1917, found byKarl Schwarzschild shortly after the discovery of generalrelativity. At first many people, including Israel himself, arguedthat since black holes had to be perfectly spherical, a blackhole could only form from the collapse of a perfectly sphericalobject. Any real star - which would never be perfectly spherical- could therefore only collapse to form a naked singularity.
There was, however, a different interpretation of Israel’sresult, which was advocated by Roger Penrose and JohnWheeler in particular. They argued that the rapid movementsinvolved in a star’s collapse would mean that the gravitationalwaves it gave off would make it ever more spherical, and bythe time it had settled down to a stationary state, it would beprecisely spherical. According to this view, any non-rotating star,however complicated its shape and internal structure, would endup after gravitational collapse as a perfectly spherical black hole,whose size would depend only on its mass. Further calculationssupported this view, and it soon came to be adopted generally.
Israel’s result dealt with the case of black holes formed fromnon-rotating bodies only. In 1963, Roy Kerr, a New Zealander,found a set of solutions of the equations of general relativitythat described rotating black holes. These “Kerr” black holesrotate at a constant rate, their size and shape depending onlyon their mass and rate of rotation. If the rotation is zero, theblack hole is perfectly round and the solution is identical to theSchwarzschild solution. If the rotation is non-zero, the blackhole bulges outward near its equator (just as the earth or thesun bulge due to their rotation), and the faster it rotates, themore it bulges. So, to extend Israel’s result to include rotatingbodies, it was conjectured that any rotating body that collapsedto form a black hole would eventually settle down to astationary state described by the Kerr solution. In 1970 acolleague and fellow research student of mine at Cambridge,Brandon Carter, took the first step toward proving thisconjecture. He showed that, provided a stationary rotating blackhole had an axis of symmetry, like a spinning top, its size andshape would depend only on its mass and rate of rotation.
Then, in 1971, I proved that any stationary rotating black holewould indeed have such an axis of symmetry. Finally, in 1973,David Robinson at Kings College, London, used Carter’s andmy results to show that the conjecture had been correct: sucha black hole had indeed to be the Kerr solution. So aftergravitational collapse a black hole must settle down into a statein which it could be rotating, but not pulsating. Moreover, itssize and shape would depend only on its mass and rate ofrotation, and not on the nature of the body that had collapsedto form it. This result became known by the maxim: “A blackhole has no hair.” The “no hair” theorem is of great practicalimportance, because it so greatly restricts the possible types ofblack holes. One can therefore make detailed models of objectsthat might contain black holes and compare the predictions ofthe models with observations. It also means that a very largeamount of information about the body that has collapsed mustbe lost when a black hole is formed, because afterward all wecan possibly measure about the body is its mass and rate ofrotation. The significance of this will be seen in the nextchapter.
Black holes are one of only a fairly small number of cases inthe history of science in which a theory was developed in greatdetail as a mathematical model before there was any evidencefrom observations that it was correct. Indeed, this used to bethe main argument of opponents of black holes: how could onebelieve in objects for which the only evidence was calculationsbased on the dubious theory of general relativity? In 1963,however, Maarten Schmidt, an astronomer at the PalomarObservatory in California, measured the red shift of a faintstarlike object in the direction of the source of radio wavescalled 3C273 (that is, source number 273 in the thirdCambridge catalogue of radio sources). He found it was toolarge to be caused by a gravitational field: if it had been agravitational red shift, the object would have to be so massiveand so near to us that it would disturb the orbits of planets inthe Solar System. This suggested that the red shift was insteadcaused by the expansion of the universe, which, in turn, meantthat the object was a very long distance away. And to bevisible at such a great distance, the object must be very bright,must, in other words, be emitting a huge amount of energy.
The only mechanism that people could think of that wouldproduce such large quantities of energy seemed to be thegravitational collapse not just of a star but of a whole centralregion of a galaxy. A number of other similar “quasi-stellarobjects,” or quasars, have been discovered, all with large redshifts. But they are all too far away and therefore too difficultto observe to provide conclusive evidence of black holes.
Further encouragement for the existence of black holes camein 1967 with the discovery by a research student at Cambridge,Jocelyn Bell-Burnell, of objects in the sky that were emittingregular pulses of radio waves. At first Bell and her supervisor,Antony Hewish, thought they might have made contact with analien civilization in the galaxy! Indeed, at the seminar at whichthey announced their discovery, I remember that they calledthe first four sources to be found LGM 1 - 4, LGM standingfor “Little Green Men.” In the end, however, they andeveryone else came to the less romantic conclusion that theseobjects, which were given the name pulsars, were in factrotating neutron stars that were emitting pulses of radio wavesbecause of a complicated interaction between their magneticfields and surrounding matter. This was bad news for writersof space westerns, but very hopeful for the small number of uswho believed in black holes at that time: it was the firstpositive evidence that neutron stars existed. A neutron star hasa radius of about ten miles, only a few times the critical radiusat which a star becomes a black hole. If a star could collapseto such a small size, it is not unreasonable to expect that otherstars could collapse to even smaller size and become blackholes.
How could we hope to detect a black hole, as by its verydefinition it does not emit any light? It might seem a bit likelooking for a black cat in a coal cellar. Fortunately, there is away. As John Michell pointed out in his pioneering paper in1783, a black hole still exerts a gravitational fierce on nearbyobjects. Astronomers have observed many systems in whichtwo stars orbit around each other, attracted toward each otherby gravity. They also observe systems in which there is onlyone visible star that is orbiting around some unseencompanion. One cannot, of course, immediately conclude thatthe companion is a black hole: it might merely be a star thatis too faint to be seen. However, some of these systems, likethe one called Cygnus X-1 (Fig. 6.2), are also strong sources ofX-rays. The best explanation for this phenomenon is thatmatter has been blown off the surface of the visible star. As itfalls toward the unseen companion, it develops a spiral motion(rather like water running out of a bath), and it gets very hot,emitting X-rays (Fig. 63). For this mechanism to work, theunseen object has to be very small, like a white dwarf, neutronstar, or black hole. From the observed orbit of the visible star,one can determine the lowest possible mass of the unseenobject. In the case of Cygnus X-l, this is about six times themass of the sun, which, according to Chandrasekhar’r result, istoo great for the unseen object to be a white dwarf. It is alsotoo large a mass to be a neutron star. It seems, therefore, thatit must be a black hole.
There are other models to explain Cygnus X-1 that do notinclude a black hole, but they are all rather far-fetched. A blackhole seems to be the only really natural explanation of theobservations. Despite this, I had a bet with Kip Thorne of theCalifornia Institute of Technology that in fact Cygnus X-1 doesnot contain a black hole! This was a form f insurance policyfor me. I have done a lot of work on black holes, and itwould all be wasted if it turned out that black holes do notexist. But in that case, I would have the consolation of winningmy bet, which would bring me four years of the magazinePrivate Eye. In fact, although the situation with Cygnus X-1 hasnot changed much since we made the bet in 1975, there isnow so much other observational evidence in favor of blackholes that I have conceded the bet. I paid the specified penalty,which was a one-year subscription to Penthouse, to the outrageof Kip’s liberated wife.
We also now have evidence for several other black holes insystems like Cygnus X-1 in our galaxy and in two neighboringgalaxies called the Magellanic Clouds. The number of blackholes, however, is almost certainly very much higher; in thelong history of the universe, many stars must have burned alltheir nuclear fuel and have had to collapse. The number ofblack holes may well be greater even than the number ofvisible stars, which totals about a hundred thousand million inour galaxy alone. The extra gravitational attraction of such alarge number of black holes could explain why our galaxyrotates at the rate it does: the mass of the visible stars isinsufficient to account for this. We also have some evidencethat there is a much larger black hole, with a mass of about ahundred thousand times that of the sun, at the center of ourgalaxy. Stars in the galaxy that come too near this black holewill be torn apart by the difference in the gravitational forceson their near and far sides. Their remains and gas that isthrown off other stars, will fall toward the black hole. As in thecase of Cygnus X-l, the gas will spiral inward and will heat up,though not as much as in that case. It will not get hot enoughto emit X rays, but it could account for the very compactsource of radio waves and infrared rays that is observed at thegalactic center.
It is thought that similar but even larger black holes, withmasses of about a hundred million times the mass of the sun,occur at the centers of quasars. For example, observations withthe Hubble telescope of the galaxy known as M87 reveal that itcontains a disk of gas 130 light-years across rotating about acentral object two thousand million times the mass of the sun.
This can only be a black hole. Matter falling into such asupermassive black hole would provide the only source ofpower great enough to explain the enormous amounts ofenergy that these objects are emitting. As the matter spiralsinto the black hole, it would make the black hole rotate in thesame direction, causing it to develop a magnetic field rather likethat of the earth. Very high-energy particles would be generatednear the black hole by the in-falling matter. The magnetic fieldwould be so strong that it could focus these particles into jetsejected outward along the axis of rotation of the black hole,that is, in the directions of its north and south poles. Such jetsare indeed observed in a number of galaxies and quasars. Onecan also consider the possibility that there might be black holeswith masses much less than that of the sun. Such black holescould not be formed by gravitational collapse, because theirmasses are below the Chandrasekhar mass limit: stars of thislow mass can support themselves against the force of gravityeven when they have exhausted their nuclear fuel. Low-massblack holes could form only if matter was compressed toenormous densities by very large external pressures. Suchconditions could occur in a very big hydrogen bomb: thephysicist John Wheeler once calculated that if one took all theheavy water in all the oceans of the world, one could build ahydrogen bomb that would compress matter at the center somuch that a black hole would be created. (Of course, therewould be no one left to observe it!) A more practical possibilityis that such low-mass black holes might have been formed inthe high temperatures and pressures of the very early universe.
Black holes would have been formed only if the early universehad not been perfectly smooth and uniform, because only asmall region that was denser than average could becompressed in this way to form a black hole. But we knowthat there must have been some irregularities, becauseotherwise the matter in the universe would still be perfectlyuniformly distributed at the present epoch, instead of beingclumped together in stars and galaxies.
Whether the irregularities required to account for stars andgalaxies would have led to the formation of a significantnumber of “primordial” black holes clearly depends on thedetails of the conditions in the early universe. So if we coulddetermine how many primordial black holes there are now, wewould learn a lot about the very early stages of the universe.
Primordial black holes with masses more than a thousandmillion tons (the mass of a large mountain) could be detectedonly by their gravitational influence on other, visible matter oron the expansion of the universe. However, as we shall learnin the next chapter, black holes are not really black after all:
they glow like a hot body, and the smaller they are, the morethey glow. So, paradoxically, smaller black holes might actuallyturn out to be easier to detect than large ones!
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