Is Einstein Still Right?

by Clifford M. Will

  Once you cross the Schwarzschild radius, however, your fate is very different. Escape is impossible. You can fire up the most powerful rocket imaginable, subject only to the normal laws of physics, but you will be unable to get out. You are pulled inexorably toward a point at the center of the object, there to be squashed to zero volume and infinite density. In desperation you send a light signal outwards, pleading for help, and indeed you witness the signal moving away from you at the speed of light. But, unbeknownst to you, that signal is actually following you inward, later to join you and everything else that ever crossed that fatal sphere in a crushing finality.

  It may seem contradictory to imagine sending a light signal outward, yet to have that signal actually follow you inward. One analogy that explains how this might work is to imagine a swimmer who always swims at a fixed speed within water, never faster, never slower. The swimmer is in the Niagara river, just above the famous waterfalls (Figure 6.1). Because her speed is higher than that of the current, she can freely swim up the river, down the river or across the river. Compared to a person treading water and following the current, she is always swimming at the same speed. But if she allows herself to go over the falls, her fate is different. She can try to swim upwards, and indeed relative to the person floating freely with the descending water, she is moving upward at her normal speed. Yet both swimmers are moving downward, to be dashed on the rocks below. Like all the analogies used in this book, this one is not perfect, but it gives a sense of how light can never escape from the Schwarzschild object. Yet contrary to what John Michell thought (see page 29), light never actually comes to rest according to anybody who measures its speed.

  Figure 6.1 A waterfall as an event horizon. Above the waterfall a person floats with the current, while a swimmer swims away from him at her fixed speed, and slowly makes her way upstream. Below the waterfall the person still flows with the current, and the swimmer still moves away from him at her standard speed, but now both are falling to the rocks below, and the swimmer will never reach the top.

  Because the Schwarzschild radius is the boundary between what can and cannot communicate with the outside world, it came to be called the “event horizon.” Just as you cannot receive light from the Sun after it falls below the Earth’s horizon, you cannot receive any signal from any event that occurs inside the Schwarzschild radius.

  By the early to mid 1960s, these kinds of results convinced many general relativists that Schwarzschild’s Massenpunkt solution was something to take seriously. John Wheeler was one of them, and in fact the term “black hole” is often credited to him. He had been ruminating on an appropriate term for these objects, and during a 1967 lecture he was giving at the Goddard Center for Space Studies in New York, he wondered aloud about a suitable name. Somebody in the audience shouted “black hole,” and Wheeler immediately adopted and promoted it.

  But to most physicists and almost all astronomers, black holes were curiosities of Einstein’s theory, but so what? That attitude began to change with the discovery of quasars.

  In the fall of 1960, Caltech astronomers Thomas Matthews and Allan Sandage prepared to use the 200 inch telescope at Mount Palomar in California to make some observations of a radio source denoted 3C48 (the forty-eighth entry in the third “Cambridge catalogue” of radio sources). They were interested in what kind of visible light this source might be emitting, so on the night of 26 September 1960 they took a photographic plate of the area of sky around 3C48. Conventional wisdom at the time told them that they would find a cluster of galaxies at the location of the radio source, but this was nothing like what they saw. Instead, as far as anyone could tell by looking at the photographic plate, the object was a star. Yet it was like no other star seen up to then, for subsequent observations during October and November of that year and periodically throughout 1961 showed that its spectrum of colors was highly unusual, and that its brightness or luminosity varied widely and rapidly, sometimes over periods as brief as 15 minutes. This was a new addition to the astronomical family, and it needed a special name. It was a powerful radio source, yet it looked “stellar” or starlike (ordinary stars are not strong radio sources); on the other hand, because of its spectrum and variability it was not quite a star, it was only “quasi” stellar. Hence the name quasistellar radio source or “quasar” was soon applied to this object and to others like it.

  The discovery of quasars brought general relativity to the attention of astronomers. The reason was an energy crisis of truly cosmic proportions. Within a few years after the discovery of 3C48, it was found that it and other quasars like it were among the most distant objects in the universe. What the astronomers thought were unusual spectra were actually rather ordinary spectra in which all the features were shifted uniformly to the red end of the frequency spectrum. This meant that the quasars must be moving away from us at high speeds, 30 percent of the speed of light in the case of 3C48. The shift in wavelength to the red is a consequence of the expansion of the universe. For 3C48, for instance, the recession velocity corresponded to a distance of about six billion light years. Because the quasars were so distant, one would have expected them to be faint, yet they were very bright sources, both in visible light and in radio waves. Therefore, their intrinsic brightness or luminosity must be enormous. For 3C48, the numbers translated into a hundred times the brightness of our own galaxy.

  This was the energy crisis: What could possibly be the source of such power? On cosmic scales the strongest force known is gravity, so it was suggested that the energy of super-strong gravitational fields could provide the answer. Furthermore, the source of this power had to be very compact, for the simple reason that for the source to vary in brightness coherently over a period of, say, one hour, it couldn’t be much larger than the distance light can travel in one hour, in order for one side of the source to know what the other side is doing and thus to behave in unison.

  Thus, one solution to the quasar energy crisis involved strong gravitational fields, meaning perhaps a huge concentration of mass, maybe millions of times the mass of the Sun, confined to a region of space smaller than a light hour, or about the diameter of the orbit of Jupiter. This represented a new collapsed state of matter that could only be described by the general theory of relativity.

  But relativists and astronomers knew almost nothing about each other, worked on entirely different problems, were housed in entirely different departments within universities, and spoke different scientific languages. To remedy this, in June 1963 a small group of relativity researchers based in Texas sent invitations to astronomers and general relativists around the world to attend a conference on a proposed new discipline, to be called relativistic astrophysics. The First Texas Symposium on Relativistic Astrophysics was held in Dallas on 16–18 December 1963 (page 5). The atmosphere was a mixture of excitement, because of the potential for solving an important problem by bringing these communities together, and grief, because of the assassination of President John Kennedy in that city just three and a half weeks earlier. Indeed, Texas Governor John Connelly, his arm still in a sling from having taken one of the assassin’s bullets, opened the conference and welcomed the participants. There were 300 attendees, of whom roughly 240 were astronomers or astrophysicists, and 60 were relativity researchers. The latter number represented almost all of the world’s general relativists at the time. The only ones missing were relativists from Eastern Europe and the Soviet Union, this being the middle of the Cold War.

  The problem of quasars took center stage, and the leading models to resolve the energy crisis involved the collapse of great masses to the Schwarzschild “singularity.” But what was collapsing? William Fowler of Caltech and Fred Hoyle of Cambridge University proposed the collapse of a supermassive star, perhaps millions of times the mass of the Sun. Cornell astronomer Thomas Gold suggested the collapse of an enormous and dense cluster of stars. John Wheeler and his post-docs and students presented papers on the collapse of compact objects such as neutron stars. It is
interesting in retrospect to notice that all the models discussed were about the collapse process, while the final Schwarzschild singularity, as it was still called, played no essential role. The concept of the black hole as a standalone object was still poorly understood in 1963, and it would be several decades before supermassive black holes would be identified as the “central engine” for the power of quasars.

  There were very few papers devoted purely to general relativity and its consequences. One, given by a young Ph.D. student of Wheeler named Kip Thorne, was on a toroidal, or donut-shaped, configuration of pure electromagnetic fields held together by gravity, a rather esoteric topic. The other was a mathematical paper by a physicist from New Zealand named Roy P. Kerr, who was working at the University of Texas at Austin. He had been using a variety of sophisticated mathematical techniques that exploited symmetry principles to look for new exact solutions of Einstein’s equations. The solution he obtained was expressed in a fairly obscure system of mathematical variables, and so when he gave his talk he must have seemed like a visitor from another planet to the astronomers, who had not yet learned how to comprehend relativistic jargon. But during the question period after his talk, the Greek relativist Achilles Papapetrou admonished the audience to pay attention to this young man’s solution, because he had a feeling it would one day prove to be important.

  Indeed, Kerr’s solution was soon identified as the exact solution for a rotating black hole and became the basis for all of modern black hole physics. Schwarzschild’s solution was for the special case of a non-rotating black hole, but, since almost everything in the universe—planets, stars, galaxies—rotates, the Kerr solution would prove to be more physically relevant.

  The fact that astronomers and general relativists were being brought together to work together on these kinds of questions was exciting, although at first it had its amusing side. Several participants at that first Texas symposium tell of a general relativity theorist interrupting a lecture by an astronomer to ask what he meant by the “magnitude” of a star (magnitude is the astronomer’s measure of the brightness of a star, an elementary concept taught in every freshman astronomy class), or of the astronomer asking the general relativist what the “Riemann tensor” was (the Riemann tensor is a measure of the curvature of spacetime, to the relativist an equally elementary concept). There were skeptics of this attempt to get the two fields to play together nicely. The MIT astrophysicist Philip Morrison proclaimed himself “interested but unpersuaded” that new physics would come out of collapse to the Schwarzschild radius, while Peter Bergmann admitted that he was “not very optimistic” that the play date between the two communities would amount to much any time soon.

  But Tommy Gold had the last laugh during his banquet speech, declaring:

  It was … [Fred] Hoyle’s genius which produced the extremely attractive idea that … the relativists, with their sophisticated work, were not only magnificent cultural ornaments, but might actually be useful to science! Everyone is pleased: the relativists, who feel they are being appreciated, who are suddenly experts in a field they hardly knew existed; the astrophysicists, for having enlarged their domain, their empire, by the annexation of another subject, general relativity. It is all very pleasing, so let us all hope that it is right. What a shame it would be if we had to go and dismiss all the relativists again!

  Soon, however, the practitioners of this new interdisciplinary field learned how to communicate with each other, so that by later Texas Symposia (the twenty-ninth was held in Cape Town, South Africa in 2017), it was not uncommon to find relativistic astrophysicists who were as knowledgable about the intricacies of curved spacetime as they were about the structure and evolution of stars or about the capabilities and limitations of X-ray telescopes.

  From 1963 to 1974, many of the key physical and mathematical properties of black holes were established during a period of intense research by a score of theorists. They learned that, to an observer outside the horizon, the only feature of the black hole itself that is detectable is its gravitational field. All information about what went across the horizon either during the formation of the black hole or during its later life is lost. Any matter or radiation that remains outside the horizon, of course, is detectable. Far away from the black hole, this gravitational field is indistinguishable from the gravitational field of any object of the same mass and angular momentum, such as a star. However, to an observer close to the horizon, things can be very unusual. The deflection of light can be so large that light can be deflected by large angles, not just a few arcseconds. A light ray can even move on a circular orbit just outside the horizon, at 1.5 times the Schwarzschild radius, for a non-rotating black hole. For the Kerr solution, the rotation of the black hole produces the same effects of the dragging of inertial frames as those induced by the rotating Earth. These are the effects confirmed by Gravity Probe-B and the LAGEOS measurements (Chapter 4). But if the observer goes close enough to the horizon, near the equator, the dragging of spacetime becomes so strong that the observer will be dragged around bodily with the rotation of the hole, no matter how hard he blasts his rockets to try to avoid whirling around the body.

  But instead of dwelling on the many unusual and remarkable properties of black holes, we will turn to the observational search for black holes, looking particularly for examples where tests of general relativity might be feasible.

  While the discovery of quasars spurred interest in the role of general relativity in astrophysics, it would be several decades before the central role of black holes in the quasar phenomenon would be appreciated. Instead, the first serious candidate for an actual black hole in nature came in 1971, from the new field of X-ray astronomy.

  The first astronomical X-rays from sources other than the Sun were discovered beginning in 1962, including a source called Cygnus X-1, the name denoting the first X-ray source found in the constellation Cygnus. By 1967 about thirty such sources were known, all detected using instruments placed on sounding rockets or balloons launched far above the Earth’s absorbing atmosphere. However, X-ray astronomy made a giant leap into the mainstream of astronomy with the launch of the Uhuru orbiting X-ray satellite in December 1970. The name Uhuru, meaning “freedom” in Swahili, was given to the satellite because it was launched from a facility in Kenya on that country’s independence day (NASA’s official name was the typically boring “X-ray Explorer Satellite SAS-A”). During its three-year lifetime, Uhuru charted more than three hundred X-ray sources. Later orbiting X-ray satellites found many more sources, including ordinary stars, white dwarfs, neutron stars, galaxies and quasars, as well as a diffuse background of X-rays, reaching us from all directions.

  Uhuru’s examination of the X-rays from Cygnus X-1 gave two crucial pieces of information that led to the conclusion that a black hole was present. The first was the observation that the X-rays were variable in time in an irregular fashion, but on timescales as short as a third of a second. This meant that the region from which the X-rays originated had to be of the order of a third of a light second, or around 100,000 kilometers in size. This, in turn, implied that the object at the center of the X-ray emitting region had to be a very compact object, such as a white dwarf, a neutron star or a black hole, because a normal star, like our Sun, would have a diameter ten times too large. The second piece of information provided by Uhuru was an accurate enough position for the source in the sky to make it possible to locate a star, known as HDE 226868, at the same location. Examination of the spectrum of light from this star showed that it was in orbit about a companion. This was determined by looking at the Doppler shifts in its spectral lines, just as the orbits of binary pulsars are determined by looking at the Doppler shifts of their pulse periods (see Chapter 5), or as exoplanets are found using Doppler shifts of the spectra of their parent stars. The companion had to be the X-ray source.

  You may be wondering exactly how a black hole meets up with a star in order to perform this dance, since after all, space is a very large and e
mpty place. The standard scenario begins before the black hole was a black hole, back when it was a star orbiting a companion star. Even though our Sun is the only star in the solar system, as many as half the stars in our galaxy are in binary systems, orbiting around each other just as Earth orbits the Sun. After a long enough period of time one of these stars will run out of fuel to burn via thermonuclear reactions, and if it is massive enough it will collapse with an accompanying supernova explosion of its outer layers. For a relatively low-mass initial star, the explosion and collapse frequently produces a neutron star. This is the pathway that can lead to pulsars in binary systems, as we discussed in Chapter 5 (page 80). But if the initial star has a higher mass, the implosion of the core does not halt at the neutron star stage but proceeds all the way to a black hole. What is left then is a black hole and a star in a binary system. Subsequently, if the stellar companion itself is massive enough, it may also eventually undergo a supernova explosion and a core implosion, leading to a black hole companion. Such binary black hole systems will be lead characters in our story of gravitational wave detection in the next three chapters.

  But back during the black hole–star phase, if the black hole is close enough to its companion star, its strong tidal gravitational force can distort the star into a shape somewhat like a teardrop (Figure 6.2). At the tip of the teardrop the force of attraction toward the black hole is stronger than that toward the star, and so gas migrates from the star toward the black hole. But the gas does not head right into the black hole, because the hole’s orbital motion has carried it sideways a bit. So just as two ice skaters passing by each other quickly lock arms and begin a rapid spin around each other, the streaming gas is grabbed by the black hole’s gravity and swirls around it in a gaseous disk. Because a ring of gas at a given distance from the black hole moves a little faster than a ring just outside it and a little slower than a ring just inside it, there is friction between adjacent rings of gas. This friction has two important consequences. It heats the gas to such high temperatures that the gas emits light all the way into the X-ray band. The friction also slows down the rings of gas, causing them to spiral inward to the black hole. When the gas reaches a distance from the hole around three times the radius of the horizon, it can no longer maintain a steady circular orbit and it plunges toward the hole, crossing the event horizon and adding a bit to the mass of the hole. This inner edge of the disk is represented by the white region in Figure 6.2. A disk like this is called an “accretion disk” because the gas eventually is accreted by the black hole.