Page 59 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 7

Figure 7:5

With primordial black holes being so scarce, it might seem unlikely that there would be one near enough for us to
observe as an individual source of gamma rays. But since gravity would draw primordial black holes toward any matter,
they should be much more common in and around galaxies. So although the gamma ray background tells us that there
can be no more than 300 primordial black holes per cubic light-year on average, it tells us nothing about how common
they might be in our own galaxy. If they were, say, a million times more common than this, then the nearest black hole
to us would probably be at a distance of about a thousand million kilometers, or about as far away as Pluto, the farthest
known planet. At this distance it would still be very difficult to detect the steady emission of a black hole, even if it was
ten thousand megawatts. In order to observe a primordial black hole one would have to detect several gamma ray
quanta coming from the same direction within a reasonable space of time, such as a week. Otherwise, they might
simply be part of the background. But Planck’s quantum principle tells us that each gamma ray quantum has a very
high energy, because gamma rays have a very high frequency, so it would not take many quanta to radiate even ten
thousand megawatts. And to observe these few coming from the distance of Pluto would require a larger gamma ray
detector than any that have been constructed so far. Moreover, the detector would have to be in space, because
gamma rays cannot penetrate the atmosphere.

Of course, if a black hole as close as Pluto were to reach the end of its life and blow up, it would be easy to detect the
final burst of emission. But if the black hole has been emitting for the last ten or twenty thousand million years, the
chance of it reaching the end of its life within the next few years, rather than several million years in the past or future,
is really rather small! So in order to have a reasonable chance of seeing an explosion before your research grant ran
out, you would have to find a way to detect any explosions within a distance of about one light-year. In fact bursts of

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