One safe way to study a black hole would be to go into orbit around it, well beyond the disruptive influence of the hole's strong tidal forces. After all, Earth and the other planets of our solar system all orbit the Sun without falling into it and without being torn apart. The gravity field around a black hole is basically no different.
However, even from a stable circular orbit, a close investigation of the hole would be unsafe for humans. Human endurance tests conducted on astronauts of the United States and the former Soviet Union indicate that the human body cannot withstand stress greater than about 10 times the pull of gravity on Earth's surface. This breaking point would occur about 3000 km from a 10—solar mass black hole (which, recall, would have a 30-km event horizon). Closer than that, the tidal effect of the hole would tear a human body apart.
Let's instead send an imaginary indestructible astronaut—a mechanical robot, say—in a probe toward the center of the hole, as illustrated in Figure 22.15. Watching from a safe distance in our orbiting spacecraft, we can then examine the nature of space and time near the hole. Our robot will be a useful explorer of theoretical ideas, at least down to the event horizon. After that boundary is crossed, there is no way for the robot to return any information about its findings.
Figure 22.15 Hypothetical robot astronauts can travel toward a black hole while performing experiments that humans, farther away, can monitor in order to learn something about the nature of space near the event horizon.
Suppose, for example, our robot has an accurate clock and a light source of known frequency mounted on it. From our safe vantage point far outside the event horizon, we could use telescopes to read the clock and measure the frequency of the light we receive. What might we discover?
We would find that the light from the robot would become more and more redshifted as the robot neared the event horizon. Even if the robot used rocket engines to remain motionless, the redshift would still be detected. The redshift is not caused by motion of the light source. It is not the result of the Doppler effect arising as the robot falls into the hole. Rather, it is a redshift induced by the black hole's gravitational field, clearly predicted by Einstein's general theory of relativity and known as gravitational redshift.
We can explain the gravitational redshift as follows. According to general relativity, photons are attracted by gravity. As a result, in order to escape from a source of gravity, photons must expend some energy: they have to work to get out of the gravitational field. They don't slow down at all—photons always move at the speed of light—they just lose energy. Because a photon's energy is proportional to the frequency of its radiation, light that loses energy must have its frequency reduced (or, conversely, its wavelength lengthened). As illustrated in Figure 22.16, radiation coming from the vicinity of a gravitating object will be redshifted by an amount depending on the strength of the gravitational field.
Figure 22.16 As a photon escapes from the strong gravitational field close to a black hole it must expend energy to overcome the hole's gravity. This energy does not come from a change in the speed at which it travels (this is always 300,000 km/s, even under these extreme conditions). Rather, the photon "gives up" energy by increasing its wavelength. Thus, the photon's color changes. This figure shows the effect on two beams of radiation, one of visible light and one of X-rays, emitted from a space probe as it nears a 1-solar mass black hole.
As photons traveled from the robot's light source to the orbiting spacecraft they would become gravitationally redshifted. From our standpoint on the orbiting spacecraft, a green light, say, would become yellow and then red as the robot astronaut neared the black hole. From the robot's perspective, the light would remain green. As the robot got closer to the event horizon, the radiation from its light source would become undetectable with optical telescopes. The radiation reaching us in the orbiting spacecraft would by then be lengthened so much that infrared and then radio telescopes would be needed to detect it. Closer still to the event horizon, the radiation emitted as visible light from the robot probe would be shifted to wavelengths even longer than conventional radio waves by the time it reached us.
Light emitted from the event horizon itself would be gravitationally redshifted to infinitely long wavelengths. In other words, each photon would use all its energy trying to escape from the edge of the hole. What was once light (on the robot) would have no energy left on arrival at the safely orbiting spacecraft. Theoretically, this radiation would reach us—still moving at the speed of light—but with zero energy. The light radiation originally emitted would be redshifted beyond our perception.
What about the robot's clock? Assuming that we could read it, what time would it tell? Would there be any observable change in the rate at which the clock ticked as it moved deeper into the hole's gravitational field? From the safely orbiting spacecraft, we would find that any clock close to the hole would appear to tick more slowly than an equivalent clock on board the spacecraft. The closer the clock came to the hole, the slower it would appear to run. The clock closest to the hole would operate slowest of all. On reaching the event horizon, the clock would seem to stop altogether. It would be as if the robot astronaut had found immortality! All action would become virtually frozen in time. Consequently, an external observer would never actually witness an infalling astronaut sink below the event horizon. Such a process would appear to take forever.
This apparent slowing down of the robot's clock is known as time dilation. It is another clear prediction of general relativity, and in fact it is closely related to the gravitational redshift. To see this connection, imagine that we use our light source as a clock, with the passage of a wave crest (say) constituting a "tick." The clock thus ticks at the frequency of the radiation. As the wave is redshifted, the frequency drops, and fewer wave crests pass the distant observer each second—the clock appears to slow down. This thought experiment demonstrates that the redshift of the radiation and the slowing of the clock are one and the same.
From the point of view of the indestructible robot, however, relativity theory predicts no strange effects at all. To the infalling robot, the light source hasn't reddened, and the clock keeps perfect time. In the robot's frame of reference, everything is normal. Nothing prohibits it from approaching within the Schwarzschild radius of the hole. No law of physics constrains an object from passing through an event horizon. There is no barrier at the event horizon and no sudden lurch as it is crossed; it is only an imaginary boundary in space. Travelers passing through the event horizon of a sufficiently massive hole (such as might lurk in the heart of our own galaxy, as we will see) might not even know it—at least until they tried to get out!
Most astronomical objects' gravitational fields are far too weak to produce any significant gravitational redshift, although in many cases the effect can still be measured. Exceedingly delicate laboratory experiments on Earth have succeeded in detecting the tiny gravitational redshift produced by even our own planet's weak gravity. Sunlight is redshifted by only about a hundredth of an angstrom. A few white-dwarf stars do show some significant reddening of their emitted light, however. Their radii are much smaller than that of our Sun, so their surface gravity is very much stronger than the Sun's. Neutron stars should show a substantial shift in their radiation, but it is currently difficult to disentangle the effects of gravity and magnetism on the observed signals.
No doubt you are wondering what lies within the event horizon of a black hole. The answer is simple: no one really knows. However, the question raises some very fundamental issues that lie at the forefront of modern physics.
Can an entire star simply shrink to a point and vanish? General relativity predicts that without some agent to compete with gravity, the core remnant of a high-mass star will collapse all the way to a point at which both its density and its gravitational field become infinite—a so-called singularity. However, we should not take this prediction of infinite density too literally. Singularities always signal the breakdown of the theory producing them. In other words, the present laws of physics are simply inadequate to describe the final moments of a star's collapse.
As it stands today, the theory of gravity is incomplete because it does not incorporate a proper (that is, a quantum-mechanical) description of matter on very small scales. As our collapsing stellar core shrinks to smaller and smaller radii we eventually lose our ability even to describe, let alone predict, its behavior. Perhaps matter trapped in a black hole never actually reaches a singularity. Perhaps it just approaches this bizarre state, in a manner that we will someday understand as the subject of quantum gravity—the merger of general relativity with quantum mechanics—develops.
Having said that, we can at least estimate how small the core can get before current theory fails. It turns out that by the time that stage is reached, the core is already much smaller than any elementary particle. Thus, although a complete description of the end-point of stellar collapse may well require a major overhaul of the laws of physics, for all practical purposes the prediction of collapse to a point is valid. Even if a new theory somehow succeeds in doing away with the central singularity, it is very unlikely that the external appearance of the hole, or the existence of its event horizon, will change. Any modifications to general relativity are expected to occur only on submicroscopic scales, not on the macroscopic (kilometer-sized) scale of the Schwarzschild radius.
Singularities are places where the rules break down, and some very strange things may occur near them. Many possibilities have been envisaged—gateways into other universes, time travel, the creation of new states of matter—but none of them has been proved, and certainly none of them has been observed. Because these regions are places where science fails, their presence causes serious problems for many of our cherished laws of physics, from causality (the idea that cause should precede effect, which runs into immediate problems if time travel is possible), to energy conservation (which is violated if material can hop from one universe to another through a black hole).
Disturbed by the possibility of such chaos in science, some relativists have even proposed a "principle of cosmic censorship": Nature always hides any singularity, such as that found at the center of a black hole, inside an event horizon. In that case, even though physics fails, that breakdown cannot affect us outside, so we are safely insulated from any effects the singularity may have. What would happen if we one day found a so-called naked singularity somewhere, a singularity uncloaked by an event horizon? Would relativity theory still hold there? For now, we just don't know.
What sense are we to make of black holes? Do black holes, and all the strange phenomena that go on in and around them, really exist? The basis for understanding these weird phenomena is the relativistic concept that mass warps space—which has already been found to be a good representation of reality, at least for the weak gravitational fields produced by stars and planets (see More Precisely 22-2). The larger the mass concentration, the greater the warping, and thus, apparently, the stranger the observational consequences. Although general relativity is not proven, there is presently no reason to disbelieve it, and black holes are one of its most striking predictions. So long as general relativity stands as the correct theory of gravity in the universe, black holes are real.
