Gravity's Engines: How Bubble-Blowing Black Holes Rule Galaxies, Stars, and Life in the Cosmos

by Scharf, Caleb

  This was an immense challenge, and it taxed Einstein to the limit. In late 1915, after a number of half-successes, he finally arrived at a mathematical description that completely encapsulated this new physics. He would not have gotten there without the work of many others, including those who essentially arrived at the very same point at the same moment. However, Einstein was the one individual whose incredible intuition and persistence broke through the layers that had obscured this improved description of the universe.

  All those years of work can be summarized in what is referred to as the Einstein field equation, a form that is surprisingly but deceptively simple:

  Equations can induce panic in many of us, but there are features of Einstein’s field equation that we can readily understand without going very deeply into its full complexity. It’s just describing all the things we have already talked about. On the left-hand side, the symbol G is the description of the curvature of space and time. On the right-hand side, the symbol T contains the description of mass and energy in the bit of spacetime in question. So, for example, T might be thought of as the instructions that describe where a spherical mass is, how massive it is, and whether it’s moving or rotating. G then contains the instructions for how you or I, or a large whale, will move in the distorted or curved spacetime around that mass. Those instructions naturally also contain the information about how coordinates and distances will work, and how time may be dilated. G is often known in technical terms as the Einstein tensor and T is known as the stress-energy tensor, easily remembered as stress is what you get when you distort or curve something.

  The second feature to pay attention to is that cluster of symbols before the T. In there is the familiar symbol for pi (π), which has a numerical value of about 3.141. The symbol G is the gravitational constant. This is a constant of nature that was also part of Newton’s original formulation of the laws of gravity. It simply describes the strength of gravity relative to all other forces, and it’s a small number: about 6.67 × 10−11, with the unit being meters cubed per kilogram, per second squared. On the bottom (the denominator) is c4, which is the speed of light multiplied by itself four times. That, by any standard, is a big number. It’s about 8 × 1033, or 8 followed by 33 zeroes, since light speed is about 300,000,000 meters per second. What this all means is that the bunch of constants in Einstein’s field equation end up as a tiny, tiny factor, and the equation becomes:

  G = 0.00000000000000000000000000000000000000000002 × T

  This isn’t just playing with the numbers—it’s telling us something very important: while spacetime can curve and is a flexible medium, it is also extremely rigid and stiff. It takes a lot of T to get a little bit of G. In other words, you need a great deal of mass or energy in a very small region to get appreciable distortion of spacetime. A large building or a big mountain doesn’t cause us to swerve in our cars or topple off our feet as we walk down the street. Indeed, it takes all 13 trillion trillion pounds of the planet Earth to keep us stuck to its surface. Even inside this curved space we can still do the high jump or throw a baseball into the air. Little wonder that the Schwarzschild radius we encountered in chapter 1 has to be so tiny in order to create the event horizon of a black hole. Matter must be packed to an incredible density to produce the enormous stress on spacetime, the T, necessary to overcome its inherent stiffness and to warp the local environment enough to trap photons of light.

  The distortion, or curvature, of spacetime described by G affects the fundamental geometry of positions, distances, and motions. I’ll refer you back to figures 3 and 4 for a reminder of how to visualize this. The bunching up of coordinates that our falling whale felt nose to tail, and the stretching from top to bottom, applies to the propagation of light as well. The electromagnetic waveforms of photons emitted just at the outside edge of the event horizon are stretched effectively flat as they climb away. In other words, they are drained of all energy, and cease to exist. Hence we can never see them escape.

  The stiffness of spacetime is connected to another phenomenon that is noticeably manifest around extremely dense collections of matter. When Karl Schwarzschild produced his solution to Einstein’s field equation for a single spherical mass and gave birth to the idea of an event horizon, he had to assume that the mass was not rotating. Yet if we look out into the universe with our eyes and our telescopes, this is not the way most objects behave. We’re well aware that the Earth spins about its axis. But the Sun also spins. All the planets and moons spin. We can measure the spin of other stars. The messy material around baby stars is rotating in great dirty wheels of dust and gas. Spiral galaxies rotate. Matter in the vast nebulae slowly drifts and moves. The periodic, often circular, motion of solid or gaseous material about a central axis is a universal phenomenon. This leads to a question that may seem obvious now, but it wasn’t always. If black holes originally form from the remnants of big old stars, what happens to their spin?

  This is particularly intriguing for two reasons. The first is that we’ve said that if a mass is packed within its Schwarzschild radius then the external universe receives no further information about it. No light escapes; no information or event can be transmitted outward. We can’t ever know what’s happening inside this horizon. The second reason is that spin is a property that is very hard to get rid of once an object has acquired it. The universe likes to preserve, or conserve, rotation. More accurately, what it likes to conserve is angular momentum. This is the mathematical product of the distribution of mass of an object with its speed of rotation. Even the most jaded physicist will refer to the simple analogy of an ice-skater to explain the concept, and it’s an analogy that works well. When ice-skaters pull their arms and legs tightly together, creating a beautiful rotation, they can speed up to a dizzying rate and wow the judges. What they’ve done is to shrink the distribution of their mass by moving it inside a smaller radius. The universe must compensate by increasing the spin, because angular momentum is conserved by nature.

  Now imagine taking an object like the Sun and compressing it to within its event horizon (its Schwarzschild radius). In its present form the Sun spins once around its axis in a regal twenty-five days, with some variation since it is not a solid body like the ice-skater. It is about 1.4 million kilometers, or 870,000 miles, in diameter. If it were to shrink to within its event horizon of about 6 kilometers, or 3.7 miles, it would have to speed up to a rate of spin at which each complete revolution would take about 0.0001 second—a ten-thousandth of a second. This sounds ridiculous, but we know that this is exactly the kind of thing that happens in nature. Neutron stars (the ultradense giant atomic nuclei left over from massive stars) can zip around in a few thousandths of a second, and as we’ve seen, these are just a short step away from being black holes. Based on what we know about real astrophysical objects, it seems inevitable that some black holes must form with enormous spin. But doesn’t the event horizon block such information from us? This was a further challenge for mathematicians and physicists trying to get a grip on this revolutionary physics.

  In the decades following Einstein’s formulation of general relativity, many scientists worked on finding new mathematical solutions to the field equation. One that eluded everyone’s efforts was a solution that would incorporate the spin of a spherical mass—the G that results from a spinning T. It was a tough nut to crack. Then, unexpectedly, in 1963, a young mathematician from New Zealand named Roy Kerr gave a brief lecture at an astrophysics conference in Dallas that changed all this. Kerr had done it. He had found a solution that went beyond that of Karl Schwarzschild, and included the possibility of a spinning object. Those who attended the meeting recall that most of the audience didn’t realize they were witnessing a moment of pure breakthrough. People dozed, and some even got up and left. But those who stayed alert were awestruck. Chandrasekhar would later write of the implications of this mathematical discovery as “the most shattering experience” in his forty-five years of doing science.

  Kerr’s solutio
n sparked a flurry of work. It quickly became clear that black hole spin was not only one of the few properties that the event horizon did not hide away, but that it would be manifest in a most remarkable fashion.

  In essence, a spinning massive object produces the same kind of effect as a tornado. The stiff and rigid spacetime surrounding the mass gets dragged around. Just as in the ferocious winds of a twister, this means that anything in the region will get dragged around, too. There is nothing you can do about it. Even light approaching a spinning black hole will end up being dragged around and around instead of immediately traveling straight down. What is most remarkable is that because this happens just outside the event horizon, the property of black hole spin is visible to the rest of the universe.

  This extraordinary characteristic led to further revelations. In 1969, the English physicist Roger Penrose argued that the energy held in a spinning black hole could be extracted. The essence of his idea can be seen by a simple example. Imagine you throw a large and crumbly brick toward the side of a black hole that is spinning away from you. At the moment the fragile brick enters the strongly dragging spacetime outside the hole, it splits into two pieces. One chunk moves on a trajectory head-on into the moving spacetime that causes it to drop to the event horizon and vanish. The other piece, however, moves in alignment with the whirling spacetime and manages to escape—like a surfer catching a wave. In Penrose’s process, the escaping chunk of brick can be moving fast enough that it carries off more energy than the entire original brick had. That extra energy comes out of the black hole’s spin.

  Again, it is because the spacetime outside the event horizon is being dragged around that the cosmos can get its sticky hands on that energy. Matter and radiation can pass this energy off into the universe by the boatload. In theory, the maximum rotational energy that can be siphoned off from a fast-spinning hole is equivalent to about 28 percent of its mass converted to pure energy. This is almost fifty times more efficient than the Sun’s production of energy by nuclear fusion in its core. In fact, black holes may be the ultimate in power-generating flywheels, and this possibility raises a critical question. Can the behavior of matter within the extreme curvature of spacetime around a black hole produce a smoking gun that actually reveals these environments to us?

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  On Earth, we have learned to extract energy from matter falling in curved spacetime. The Hoover Dam is a wonderful example of this, as is any hydroelectric plant. In the case of the Hoover Dam, billions of gallons of water accelerated to high speeds push against the blades of huge turbines that convert the energy of motion into electrical current. Out in the universe, if matter falls into the curved spacetime around a mass—sometimes described as a gravity well—it too gains speed, and gains what we call kinetic energy. This accelerating matter can then collide or interact with other falling matter along the way. Like water pouring down a slide, it churns and froths as it splashes and crashes into itself. Some of the kinetic energy gets converted into other forms. Everything from photons to subatomic particles can be spewed forth by fast-moving matter with high kinetic energy. Not surprisingly, the amount of kinetic energy gained by falling matter increases with the amount of mass in a system. The amount of energy also critically depends on how far an object can fall, how close it can get to the bottom of a gravity well. This is a factor that, as we will see, places black holes apart from anything else in the cosmos.

  Suppose we could mischievously drop a potted plant, perhaps a nice geranium, from the location of the Earth and have it fall toward the Sun, starting from a standstill and ignoring Earth’s pull. The Sun is a long way off. It is as if we’re dropping something down a 93-million-mile-deep pit. By the time our dropped pot reaches the outer solar atmosphere, it will have gained a considerable amount of kinetic energy. It will hit the visible surface of the Sun with a terminal velocity of about 370 miles a second. If the plant in its pot has a mass of one kilogram, or a little over two pounds, the kinetic energy it carries is even more astonishing. It is equivalent to the energy of 100 billion apples being dropped from one meter above the surface of the Earth. That’s also equivalent to about twenty tons of explosive energy, enough to level a small town.

  Yet this is proverbial peanuts in cosmic terms. Let’s suppose that instead of dropping our pot into the Sun, we dropped it from the same distance (one astronomical unit, or AU) toward a white dwarf, the dense remains of a once-proud star. A moderately large white dwarf with the same mass as the Sun will have a radius that is about a hundredth that of the Sun. This is key to understanding the energy gained by falling into gravity wells. The deeper you can get, the dramatically greater the kinetic energy you will gain. In this case our little pot will hit the white dwarf with a hundred times more energy than it hit the Sun with, even though the total masses of the Sun and the white dwarf are identical. It will be moving at about 6,000 kilometers (3,700 miles) a second, or 2 percent of the speed of light, and will crash down with the energy of a 2-kiloton nuclear bomb. This is all from just being dropped and allowed to fall along the shortest path in the curved spacetime around the white dwarf. It’s a cosmic game of water balloons, or flowerpots, dropped onto an unsuspecting passerby.

  If we performed the same experiment on a neutron star, which is only about six miles in radius, the result would be even more extreme. With end velocities approaching 30 percent of the speed of light, we would have to modify our estimates of the final energy of impact to properly account for the effects of special relativity, according to which our nice little pot would appear to gain inertial mass as it sped up.

  What about the ultimate extreme, a solar-mass object squeezed to a radius within its event horizon of three kilometers (1.86 miles), making a black hole? We may be giddy with anticipation, but we actually already know what will happen to our two pounds of pot, soil, and plant: falling from a distance, it will accelerate ever closer to the speed of light itself, reaching that ultimate velocity right at the event horizon. But there is no true surface for it to hit, no place to release all that kinetic energy. Furthermore, the distortion of space and time in the immediate vicinity of the event horizon becomes so extreme that what we might see as a distant observer becomes rather confusing. Our information arrives in the form of photons from the flowerpot that have climbed out of the fiercely curved spacetime around the hole. These are increasingly redshifted and diminished in energy as the pot descends to the horizon. Not only that, but the passage of time for the flowerpot appears ever slower to us as it approaches the black hole. That final explosive “pop” will never come.

  Figure 7. An illustration of the terminal velocity of objects dropped toward equal-mass astrophysical bodies from a great distance. The more compact the body, the deeper into its gravity well objects fall before hitting its surface, and the more they accelerate before they hit. The Sun is almost 435,000 miles in radius, and objects will hit it at 0.2 percent of the speed of light. A white dwarf of the same mass as the Sun is about 4,350 miles in radius, and objects hit it at 2 percent of the speed of light. A neutron star of this mass is only 6 miles in radius, and objects hit at about 30 percent the speed of light. The event horizon of a black hole of the same mass is less than 2 miles in radius, and the terminal velocity would technically be the speed of light itself (shown here as the value 1).

  Nonetheless, the mass will be moving at a tremendous speed on its way down, well before the event horizon and the shroud of these relativistic effects. If the black hole is spinning and sweeping the pot around and around, the result is further amplified. Should the pot intersect and collide with anything on the way, the potential exists for an enormous release of kinetic energy, converted into the motion of atomic and subatomic particles and electromagnetic radiation. Produced well before reaching the event horizon, these particles and photons can escape, surging back out into the universe. A crude analogy is to liken this to water draining noisily from a bathtub. As the liquid falls down into the drainpipe, some of its swirling kinetic energy
is converted into sound waves, water bashing against molecules of air. The sound waves move faster than the water, and they escape. That gurgling sound we hear comes from the energy of the moving water converted to the movement of molecules in air. This movement is transmitted from molecule to molecule, like a line of falling dominoes, and the pressure beats against our eardrums. Finally, our ears convert those forces of movement into electrical impulses that flow off into our brain.

  This generation of outgoing energy as matter moves in distorted spacetime is a defining characteristic of our universe. Mass stresses and curves spacetime around itself, and like the water falling through the channels of the Hoover Dam, matter falling into such a place can gain and release energy, lots and lots of it. It’s a very efficient process, and it gets more efficient the more distorted spacetime is. Black holes represent an ultimate extreme of this, so compact that they pull the universe in after themselves and even drag it around and around as they spin. The next key part of our story is exactly how we detect the energy produced as matter approaches the gravitational drainpipe of a black hole. Without some equivalent of the noisy slurps of escaping bathwater, black holes would remain hidden away, lurking in the dark corners of the cosmos. Luckily for us, the real situation is very different.