Page 58 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 7
2.7º above absolute zero), so such black holes would emit even less than they absorb. If the universe is destined to go
on expanding forever, the temperature of the microwave radiation will eventually decrease to less than that of such a
black hole, which will then begin to lose mass. But, even then, its temperature would be so low that it would take about
a million million million million million million million million million million million years (1 with sixty-six zeros after it) to
evaporate completely. This is much longer than the age of the universe, which is only about ten or twenty thousand
million years (1 or 2 with ten zeros after it). On the other hand, as mentioned in Chapter 6, there might be primordial
black holes with a very much smaller mass that were made by the collapse of irregularities in the very early stages of
the universe. Such black holes would have a much higher temperature and would be emitting radiation at a much
greater rate. A primordial black hole with an initial mass of a thousand million tons would have a lifetime roughly equal
to the age of the universe. Primordial black holes with initial masses less than this figure would already have
completely evaporated, but those with slightly greater masses would still be emitting radiation in the form of X rays and
gamma rays. These X rays and gamma rays are like waves of light, but with a much shorter wavelength. Such holes
hardly deserve the epithet black: they really are white hot and are emitting energy at a rate of about ten thousand
megawatts.

One such black hole could run ten large power stations, if only we could harness its power. This would be rather
difficult, however: the black hole would have the mass of a mountain compressed into less than a million millionth of an
inch, the size of the nucleus of an atom! If you had one of these black holes on the surface of the earth, there would be
no way to stop it from falling through the floor to the center of the earth. It would oscillate through the earth and back,
until eventually it settled down at the center. So the only place to put such a black hole, in which one might use the
energy that it emitted, would be in orbit around the earth – and the only way that one could get it to orbit the earth
would be to attract it there by towing a large mass in front of it, rather like a carrot in front of a donkey. This does not
sound like a very practical proposition, at least not in the immediate future.
But even if we cannot harness the emission from these primordial black holes, what are our chances of observing
them? We could look for the gamma rays that the primordial black holes emit during most of their lifetime. Although the
radiation from most would be very weak because they are far away, the total from all of them might be detectable. We
do observe such a background of gamma rays: Figure 7:5 shows how the observed intensity differs at different
frequencies (the number of waves per second). However, this background could have been, and probably was,
generated by processes other than primordial black holes. The dotted line in Figure 7:5 shows how the intensity should
vary with frequency for gamma rays given off by primordial black holes, if there were on average 300 per cubic
light-year. One can therefore say that the observations of the gamma ray background do not provide any positive
evidence for primordial black holes, but they do tell us that on average there cannot be more than 300 in every cubic
light-year in the universe. This limit means that primordial black holes could make up at most one millionth of the
matter in the universe.

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