| Some attempts to understand gravity on a microscopic scale suggest that black holes may not be entirely black after all. Applying what they know of subatomic physics, scientists now believe it possible that some matter and radiation can escape from a black hole. Here's how. The laws of quantum physics allow a process known as pair creation to occur anywhere in space: a particle and its antiparticle—an electron and a positron, say—can come into being spontaneously, literally formed out of nothing. This, of course, violates one of the most cherished laws of physics, the law of conservation of mass and energy (recall from Section 16.5 that mass and energy are equivalent, related to each other by Einstein's famous equation E = mc2), but this violation is permitted if the "books are balanced" by the disappearance of the particles (by mutual annihilation) within a short enough period of time. In effect, the rules can be broken, so long as they are repaired before anyone notices.
Most of the time, pairs of particles appear and disappear so rapidly that energy is conserved on all macroscopic scales. However, should pair creation happen near a black hole, as illustrated in the diagram, it is possible for one of the two particles to cross the event horizon before it meets and annihilates its partner. The other particle would then be free to leave the scene, making the black hole appear to the outside world as a source of matter or radiation. The energy required to create the new particle ultimately comes from the black hole. Because energy and mass are equivalent, this means that the hole must decrease in mass as it radiates. Thus, black holes do not last forever—they slowly "evaporate." This possibility was first realized by Cambridge University mathematician Stephen Hawking. The radiation from a black hole is known as Hawking radiation.
A remarkable result, also discovered by Hawking's group, is that the spectrum of Hawking radiation is described by exactly the same curve that characterizes emission from any hot body. Black holes emit blackbody radiation! The temperature of the radiation turns out to be |
inversely related to the mass of the hole. Big black holes are very cold, whereas small black holes are hot. A hole the mass of the Sun would emit radiation at a temperature of 10-6 K; one the mass of a mountain—about 1012 kg—would have a temperature of some 1012 K. Knowing a black hole's temperature T and surface area A (of the event horizon), we can calculate its luminosity L in exactly the same way as for stars: L  AT4.  (Sec. 17.3)
A black hole radiates energy (and hence mass) into space. As the hole radiates, its mass drops and its temperature increases. That is, the black hole's temperature is inversely proportional to its mass, and its area is proportional to the square of its mass. The black hole, then, increases its luminosity as it evaporates. The increased luminosity, in turn, leads to a faster loss of mass. This runaway situation eventually ends violently, and the black hole explodes in a burst of gamma rays.
The lifetime of a hole depends on its mass. For a 1—solar mass black hole, the explosion is predicted to occur after about 1070 years! Astronomers today hardly expect to observe such an event. Thus, the issue of evaporation is moot for the black holes described in this chapter; astronomers do not expect ever to observe either their slow decay (which begins the moment they form) or their eventual explosion.
However, very small black holes, with masses of about 1012 kg, should have lifetimes roughly equal to the current age of the universe. Although we know of no way in which such objects could be created in the universe today, it is conceivable that conditions in the very earliest epochs of the universe might have been just right to compress pockets of matter into miniature black holes. Such black holes would have Schwarzschild radii of about 10-15 m, comparable to the size of a subatomic particle. If they exist, they should be exploding right now. Attempts have been made to observe the resultant gamma rays, so far without success. |
