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Black holes that have masses much less than a solar mass are called mini black holes. We think that mini black holes might have formed when the density of the universe was much higher than it is now. (The conditions in the early universe will be discussed in Chapter 21.) These may still exist. The British physicist Stephen Hawking has found that there is a mechanism by which mini black holes could actually evaporate. Hawking is studying the relationship between gravity and quantum mechanics, and the process he has proposed is a quantum mechanical one.

This mechanism involves a different concept of a vacuum than we are accustomed to seeing. In classical physics, a vacuum is simply nothing. In quantum mechanics it is possible to make something out of nothing, if you don't do it for long. It amounts to borrowing energy for a brief time interval. The more energy you borrow, the less time you can borrow it for. It is related to the uncertainty principle (which we discussed in Chapter 3). We have talked about the uncertainty principle as it relates to momentum and position. However, it also relates to energy and the lifetime of a state. It says that if the state has a lifetime At, then the energy of the state is uncertain by an amount DĹ, given by

The longer lived a state, the more accurately its energy can be determined. Since the energy of a state is uncertain by DĹ, it is possible for us to have this extra amount of energy and not detect it..

As a result of the uncertainty principle, a quantum mechanical vacuum is a very busy place. At any place it is possible to create a particle-antiparticle pair (Fig. 8.14). (We will discuss antiparitcles in Chapter 21.)

It requires an energy equal to 2mc2, where ň is the mass of the particle (and the antiparticle). The pair can exist for at most a time h/[(2p)mń2]. Before the time is up, they must find each other and annihilate. Since electrons have masses that are much less than protons, an electron-positron (antielectron) pair will live longer than a proton-antiproton pair. We can therefore think of a vacuum as being made up of continuously appearing and disappearing electron-positron pairs (with a small contribution from heavier particle-antiparticle pairs). The phenomenon is called vacuum polarization.

When an electron-positron pair is created just outside a black hole, it is possible for one of the particles to be pulled into the black hole before the two recombine. The other particle will continue moving away from the black hole. The two cannot recombine. The particles then exist for much longer than the time limit for violating conservation of energy. We must therefore make up the energy from somewhere. This process actually reduces the mass of the black hole. The black hole shrinks slightly. For mini black holes this energy loss can be a significant fraction of the mass of the black hole. Eventually, the black hole shrinks to the point where it disappears in a small burst of gamma radiation. The more massive a black hole is when it starts out, the longer it will live. An estimate for the lifetime of a black hole of mass M (in grams) is (10-26 s)(M3). So, a black hole of about 1014 g would have a liftime of about 1010 yr, a little less than the age of the universe. In the lifetime of the universe, black holes smaller than some given mass should have disappeared. Those at that mass should just be dying now. Some physicists have suggested that when this happens we should be able to see the burst of gamma radiation.

At the other end of the mass scale, much larger than stellar black holes, are maxi black holes. They probably result from large amounts of material gathering together in a small region. In Chapter 19, we will see evidence for 108 to 109 MQ black holes being present in the centers of many galaxies.