Modern notions about black holes rest squarely on the theory of relativity. Although white dwarfs and (to a lesser extent) neutron stars can be adequately described by the classical Newtonian theory of gravity, only the modern Einsteinian theory of relativity can properly account for the bizarre physical properties of black holes.
A central concept of general relativity (see More Precisely 22-1) is this: matter—all matter—tends to "warp" or curve space in its vicinity. Objects such as planets and stars react to this warping by changing their paths. In the Newtonian view of gravity, particles move on curved trajectories because they feel a gravitational force. In Einsteinian relativity, those same particles move on curved trajectories because they are following the curvature of space produced by some nearby massive object. The more the mass, the greater the warping. Close to a black hole, the gravitational field becomes overwhelming and the curvature of space extreme. At the event horizon itself, the curvature is so great that space "folds over" on itself, causing objects within to become trapped and disappear.
Some props may help you visualize the curvature of space near a black hole. Bear in mind, however, that these props are not real but only tools to help you grasp some exceedingly strange concepts.
First, imagine a pool table with the tabletop made of a thin rubber sheet rather than the usual hard felt. As Figure 22.12 suggests, such a rubber sheet becomes distorted when a heavy weight, such as a rock, is placed on it. The otherwise flat sheet sags (becomes distorted), especially near the rock. The heavier the rock, the larger the distortion. Trying to play pool, you would quickly find that balls passing near the rock were deflected by the curvature of the tabletop. In much the same way, both matter and radiation are deflected by the curvature of space near a star. For example, Earth's orbital path is governed by the relatively gentle curvature of space created by our Sun. The more massive the object, the more the space surrounding it is curved.
Figure 22.12 A pool table made of a thin rubber sheet sags when a weight is placed on it. Likewise, space is bent, or warped, in the vicinity of any massive object.
Let's consider another analogy. Imagine a large extended family of people living on a huge rubber sheet—a sort of gigantic trampoline. Deciding to hold a reunion, they converge on a given place at a given time. As shown in Figure 22.13, one person remains behind, not wishing to attend. He keeps in touch with his relatives by means of "message balls" rolled out to him (and back from him) along the surface of the sheet. These message balls are the analog of radiation carrying information through space.
Figure 22.13 Any mass causes the rubber sheet (space) to be curved. As people assemble at the appointed spot on the sheet the curvature grows progressively larger, as shown in frames (a), (b), and (c). The blue arrows represent some directions in which information can be transmitted from place to place. The people are finally sealed inside the bubble (d), forever trapped and cut off from the outside world.
As the people converge, the rubber sheet sags more and more. Their accumulating mass creates an increasing amount of space curvature. The message balls can still reach the lone person far away in nearly flat space, but they arrive less frequently as the sheet becomes more and more warped and stretched—as shown in Figures 22.11(b) and (c)—and the balls have to climb out of a deeper and deeper well. Finally, when enough people have arrived at the appointed spot, the mass becomes too great for the rubber to support them. As illustrated in Figure 22.13(d), the sheet pinches off into a "bubble," compressing the people into oblivion and severing their communications with the lone survivor outside. This final stage represents the formation of an event horizon around the party.
Right up to the end—the pinching off of the bubble—two-way communication is possible. Message balls can reach the outside from within (but at a slower and slower rate as the rubber stretches), and messages from outside can get in without difficulty. However, once the event horizon (the bubble) forms, balls from the outside can still fall in, but they can no longer be sent back out to the person left behind, no matter how fast they are rolled. They cannot make it past the "lip" of the bubble in Figure 22.13(d). This analogy (very) roughly depicts how a black hole warps space completely around on itself, isolating its interior from the rest of the universe. The essential ideas—the slowing down and eventual cessation of outward-going signals and the one-way nature of the event horizon once it forms—all have clear parallels in the case of stellar black holes.
Black holes are not cosmic vacuum cleaners. They don't cruise around interstellar space, sucking up everything in sight. The orbit of an object near a black hole is essentially the same as its orbit near a star of the same mass. Only if the object happens to pass within a few Schwarzschild radii (perhaps 50 or 100 km for a typical black hole formed in a supernova explosion) of the event horizon is there any significant difference between its actual orbit and the one predicted by Newtonian gravity and described by Kepler's laws. From a distance, the main observational difference is that an object orbiting a black hole appears to orbit a dark, empty region of space.
Black holes, then, do not go out of their way to drag in matter. However, if some matter does happen to fall into one—if its orbit happens to take it too close to the event horizon—it will be unable to get out. Black holes are like turnstiles, permitting matter to flow in only one direction—inward. A black hole's mass never decreases (but see More Precisely 22-3). Because a black hole will accrete at least a little material from its surroundings, its mass tends to increase over time. The black hole's size is proportional to its mass, so the radius of the event horizon grows with time.
Matter flowing into a black hole is subject to great tidal stress. An unfortunate person falling feet first into a solar-mass black hole would find herself stretched enormously in height and squeezed unmercifully laterally. She would be torn apart even before she reached the event horizon, for the pull of gravity would be much stronger at her feet (which are closer to the hole) than at her head. The tidal forces at work in and near a black hole are the same phenomenon responsible for ocean tides on Earth and the spectacular volcanoes on Io. The only difference is that the tidal forces near a black hole are far stronger than any force we know in the solar system.
As shown in Figure 22.14, a similar fate awaits any kind of matter falling into a black hole. Whatever falls in—gas, people, space probes—is vertically stretched and horizontally squeezed, in the process being accelerated to high speeds. The net result of all this stretching and squeezing is numerous and violent collisions among the torn-up debris, causing a great deal of frictional heating of the infalling matter. Material is simultaneously torn apart and heated to high temperatures as it plunges into the hole.
Figure 22.14 Any matter falling into the clutches of a black hole will become severely distorted and heated. This sketch shows an imaginary planet being pulled apart by the gravitational tides of the black hole.
The rapid heating of matter by tides and collisions is so efficient that, prior to submersion below the hole's event horizon, the matter emits radiation on its own accord. For a black hole of solar mass, the energy is expected to be emitted in the form of X-rays. In effect, the gravitational energy of matter outside the black hole is converted into heat while that matter falls toward the hole. Once the hot matter falls below the event horizon, its radiation is no longer detectable—it never leaves the hole. Contrary to what we might expect from an object whose defining property is that nothing can escape from it, the region surrounding a black hole is expected to be a source of energy. More Precisely 22-3 describes another, quite different, way in which a black hole can produce energy.
