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.
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 gamma rays from space have been detected by satellites originally constructed to look for violations of the Test Ban Treaty. These seem to occur about sixteen times a month and to be roughly uniformly distributed in direction across the sky. This indicates that they come from outside the Solar System since otherwise we would expect them to be concentrated toward the plane of the orbits of the planets. The uniform distribution also indicates that the sources are either fairly near to us in our galaxy or right outside it at cosmological distances because otherwise, again, they would be concentrated toward the plane of the galaxy. In the latter case, the energy required to account for the bursts would be far too high to have been produced by tiny black holes, but if the sources were close in galactic terms, it might be possible that they were exploding black holes. I would very much like this to be the case but I have to recognize that there are other possible explanations for the gamma ray bursts, such as colliding neutron stars. New observations in the next few years, particularly by gravitational wave detectors like LIGO, should enable us to discover the origin of the gamma ray bursts.