e universe. This would offer great possibilities for travel inspace and time, but unfortunately it seems that the solutions may all be high-ly unstable. The least disturbance, such as the presence of an astronaut, maychange them so that the astronaut cannot see the singularity until he hits itand his time comes to an end. In other words, the singularity always lies in hisfuture and never in his past.The strong version of the cosmic censorship hypothesis states that in a realis-tic solution, the singularities always lie either entirely in the future, like thesingularities of gravitational collapse, or entirely in the past, like the big bang.It is greatly to be hoped that some version of the censorship hypothesis holds,because close to naked singularities it may be possible to travel into the past.While this would be fine for writers of science fiction, it would mean that noone’s life would ever be safe. Someone might go into the past and kill yourfather or mother before you were conceived.In a gravitational collapse to form a black hole, the movements would bedammed by the emission of gravitational waves. One would therefore expectthat it would not be too long before the black hole would settle down to a sta-tionary state. It was generally supposed that this final stationary state woulddepend on the details of the body that had collapsed to form the black hole.The black hole might have any shape or size, and its shape might not even befixed, but instead be pulsating.However, in 1967, the study of black holes was revolutionized by a paper writ-ten in Dublin by Werner Israel. Israel showed that any black hole that is notrotating must be perfectly round or spherical. Its size, moreover, would dependonly on its mass. It could, in fact, be described by a particular solution ofEinstein’s equations that had been known since 1917, when it had been foundby Karl Schwarzschild shortly after the discovery of general relativity. At first,Israel’s result was interpreted by many people, including Israel himself, as evi-dence that black holes would form only from the collapse of bodies that wereperfectly round or spherical. As no real body would be perfectly spherical, thismeant that, in general, gravitational collapse would lead to naked singularities.There was, however, a different interpretation of Israel’s result, which wasadvocated by Roger Penrose and John Wheeler in particular. This was that ablack hole should behave like a ball of fluid. Although a body might start offin an unspherical state, as it collapsed to form a black hole it would settle downto a spherical state due to the emission of gravitational waves. Further calcu-lations supported this view and it came to be adopted generally.Israel’s result had dealt only with the case of black holes formed from nonro-tating bodies. On the analogy with a ball of fluid, one would expect that ablack hole made by the collapse of a rotating body would not be perfectlyround. It would have a bulge round the equator caused by the effect of the rota-tion. We observe a small bulge like this in the sun, caused by its rotation onceevery twenty-five days or so. In 1963, Roy Kerr, a New Zealander, had found aset of black-hole solutions of the equations of general relativity more generalthan the Schwarzschild solutions. These “Kerr” black holes rotate at aconstant rate, their size and shape depending only on their mass and rate ofrotation. If the rotation was zero, the black hole was perfectly round and thesolution was identical to the Schwarzschild solution. But if the rotation wasnonzero, the black hole bulged outward near its equator. It was therefore nat-ural to conjecture that a rotating body collapsing to form a black hole wouldend up in a state described by the Kerr solution.In 1970, a colleague and fellow research student of mine, Brandon Carter, tookthe first step toward proving this conjecture. He showed that, provided a sta-tionary rotating black hole had an axis of symmetry, like a spinning top, its sizeand shape would depend only on its mass and rate of rotation. Then, in 1971,I proved that any stationary rotating black hole would indeed have such anaxis of symmetry. Finally, in 1973, David Robinson at Kings College, London,used Carter’s and my results to show that the conjecture had been correct:Such a black hole had indeed to be the Kerr solution.So after gravitational collapse a black hole must settle down into a state inwhich it could be rotating, but not pulsating. Moreover, its size and shapewould depend only on its mass and rate of rotation, and not on the nature ofthe body that had collapsed to form it. This result became known by themaxim “A black hole has no hair.” It means that a very large amount of infor-mation about the body that has collapsed must be lost when a black hole isformed, because afterward all we can possibly measure about the body is itsmass and rate of rotation. The significance of this will be seen in the next lec-ture. The no-hair theorem is also of great practical importance because it sogreatly restricts the possible types of black holes. One can therefore makedetailed models of objects that might contain black holes, and compare thepredictions of the models with observations.Black holes are one of only a fairly small number of cases in the history of sci-ence where a theory was developed in great detail as a mathematical modelbefore there was any evidence from observations that it was correct. Indeed,this used to be the main argument of opponents of black holes. How could onebelieve in objects for which the only evidence was calculations based on thedubious theory of general relativity?In 1963, however, Maarten Schmidt, an astronomer at the Mount PalomarObservatory in California, found a faint, starlike object in the direction of thesource of radio waves called 3C273-that is, source number 273 in the thirdCambridge catalog of radio sources. When he measured the red shift of theobject, he found it was too large to be caused by a gravitational field: If it hadbeen a gravitational red shift, the object would have to be so massive and sonear to us that it would disturb the orbits of planets in the solar system. Thissuggested that the red shift was instead caused by the expansion of the uni-verse, which in turn meant that the object was a very long way away. And tobe visible at such a great distance, the object must be very bright and must beemitting a huge amount of energy.The only mechanism people could think of that would produce such largequantities of energy seemed to be the gravitational collapse not just of a starbut of the whole central region of a galaxy. A number of other similar “quasi-stellar objects,” or quasars, have since been discovered, all with large red shifts.But they are all too far away, and too difficult, to observe to provide conclu-sive evidence of black holes.Further encouragement for the existence of black holes came in 1967 with thediscovery by a research student at Cambridge, Jocelyn Bell, of some objects inthe sky that were emitting regular pulses of radio waves. At first, Jocelyn andher supervisor, Anthony Hewish, thought that maybe they had made contactwith an alien civilization in the galaxy. Indeed, at the seminar at which theyannounced their discovery, I remember that they called the first four sourcesto be found LGM 1-4, LGM standing for “Little Green Men.”In the end, however, they and everyone else came to the less romantic conclu-sion that these objects, which were given the name pulsars, were in fact justrotating neutron stars. They were emitting pulses of radio waves because of acomplicated indirection between their magnetic fields and surrounding matter.This was bad news for writers of space westerns, but very hopeful for the smallnumber of us who believed in black holes at that time. It was the first positiveevidence that neutron stars existed. A neutron star has a radius of about tenmiles, only a few times the critical radius at which a star becomes a black hole.If a star could collapse to such a small size, it was not unreasonable to expectthat other stars could collapse to even smaller size and become black holes.How could we hope to detect a black hole, as by its very definition it does notemit any light? It might seem a bit like looking for a black cat in a coal cellar.Fortunately, there is a way, since as John Michell pointed out in his pioneer-ing paper in 1783, a black hole still exerts a gravitational force on nearbyobjects. Astronomers have observed a number of systems in which two starsorbit around each other, attracted toward each other by gravity. They alsoobserved systems in which there is only one visible star that is orbiting aroundsome unseen companion.One cannot, of course, immediately conclude that the companion is a blackhole. It might merely be a star that is too faint to be seen. However, some ofthese systems, like the one called Cygnus X-I, are also strong sources of X rays.The best explanation for this phenomenon is that the X rays are generated bymatter that has been blown off the surface of the visible star. As it falls towardthe unseen companion, it develops a spiral motion-rather like water runningout of a bath-and it gets very hot, emitting X rays. For this mechanism towork, the unseen object has to be very small, like a white dwarf, neutron star,or black hole.Now, from the observed motion of the visible star, one can determine the low-est possible mass of the unseen object. In the case of Cygnus X-I, this is aboutsix times the mass of the sun. According to Chandrasekhar’s result, this is toomuch for the unseen object to be a white dwarf. It is also too large a mass tobe a neutron star. It seems, therefore, that it must be a black hole.There are other models to explain Cygnus X-I that do not include a blackhole, but they are all rather far-fetched. A black hole seems to be the onlyreally natural explanation of the observations. Despite this, I have a bet withKip Thorne of the California Institute of Technology that in fact Cygnus X-Idoes not contain a black hole. This is a form of insurance policy for me. I havedone a lot of work on black holes, and it would all be wasted if it turned outthat black holes do not exist. But in that case, I would have the consolation ofwinning my bet, which would bring me four years of the magazine Private Eye.If black holes do exist, Kip will get only one year of Penthouse, because whenwe made the bet in 1975, we were 80 percent certain that Cygnus was a blackhole. By now I would say that we are about 95 percent certain, but the bet hasyet to be settled.There is evidence for black holes in a number of other systems in our galaxy,and for much larger black holes at the centers of other galaxies and quasars.One can also consider the possibility that there might be black holes withmasses much less than that of the sun. Such black holes could not be formedby gravitational collapse, because their masses are below the Chandrasekharmass limit. Stars of this low mass can support themselves against the force ofgravity even when they have exhausted their nuclear fuel. So, low-mass blackholes could form only if matter were compressed to enormous densities by verylarge external pressures. Such conditions could occur in a very big hydrogenbomb. The physicist John Wheeler once calculated that if one took all theheavy water in all the oceans of the world, one could build a hydrogen bombthat would compress matter at the center so much that a black hole would becreated. Unfortunately, however, there would be no one left to observe it.A more practical possibility is that such low-mass black holes might have beenformed in the high temperatures and pressures of the very early universe. Blackholes could have been formed if the early universe had not been perfectlysmooth and uniform, because then a small region that was denser than aver-age could be compressed in this way to form a black hole. But we know thatthere must have been some irregularities, because otherwise the matter in theuniverse would still be perfectly uniformly distributed at the present epoch,instead of being clumped together in stars and galaxies.Whether or not the irregularities required to account for stars and galaxieswould have led to the formation of a significant number of these primordialblack holes depends on the details of the conditions in the early universe. Soif we could determine how many primordial black holes there are now, wewould learn a lot about the very early stages of the universe. Primordial blackholes with masses more than a thousand million tons-the mass of a largemountain-could be detected only by their gravitational influence on othervisible matter or on the expansion of the universe. However, as we shalllearn in the next lecture, black holes are not really black after alclass="underline" They glowlike a hot body, and the smaller they are, the more they glow. So, paradoxi-cally, smaller black holes might actually turn out to be easier to detect thanlarge ones.