A Brief History of Time: Chapter 7 Summary & Analysis

Before 1970, Hawking’s work mainly focused on the big bang. Around the time of his daughter’s birth, he thought about black holes and their event horizon, a not very well-understood idea at the time, as he was getting into bed. Hawking realized the paths of trapped light in the event horizon could never cross, or they would fall into the black hole. As such, the light at the event horizon must be moving parallel to or away from every other ray. The event horizon could only ever remain stationary or grow.

This non-decreasing nature of black holes determines much of their behavior. Penrose agreed with Hawking, and they determined a black hole’s area could be determined by its event horizon. This non-decreasing idea sounded like entropy, or disorder, which the second law of thermodynamics states never decreases. For example, gas molecules held in one half of a box by a divide will spread into the whole box when the partition is removed. The most probable outcome is that particles will spread, and thus increase disorder.

Jacob Bekenstein suggested a black hole’s entropy could be measured by its event horizon. As matter fell into the black hole the event horizon would expand, so sum of the area of black holes’ event horizons and entropy outside black holes would never decrease.

This maintained the law of entropy, but suggested that black holes ought to have a temperature, meaning it must emit radiation—but black holes aren’t meant to emit anything. Hawking, Carter, and Jim Bardeen wrote a paper in 1972 to challenge Bekenstein’s finding. Hawking partially did so in irritation because he thought Bekenstein’s had misused his work. Though, in the end, it turned out Bekenstein was right.

Hawking went to Moscow in 1973, where he met Yakov Zeldovich and Alexander Starobinsky. They convinced Hawking that rotating black holes ought to emit particles based on the uncertainty principle. When Hawking later did the mathematics to investigate it, he found even non rotating black holes ought to emit radiation. But, he didn’t want Bekenstein to find out.

Hawking finally came round to the idea because the spectrum of radiation emitted would be the same as any other hot body, and black holes seemed to obey entropy. Others have since confirmed the results, and black holes are now known to have a temperature proportional to their mass.

In fact, the particles emitted do not come from the black hole itself, but the supposedly the empty space just outside the event horizon. This space is not actually empty—there are certain minimum fluctuations and uncertainty. Pairs of particles and virtual particles will appear and collide, annihilating each other. One will have positive energy, the other negative. The real particle is always positive in normal circumstances, but the energy taken to avoid the black hole could make it have negative energy. The negative virtual particle could fall toward the black hole, become a real particle, and no longer need to annihilate with its partner. Both particles might now fall into the black hole, or the now positive-energy former-virtual particle might escape, meaning it appears that a new real particle has been emitted. Smaller black holes are easier to escape, and so seem to emit more particles and glow hotter.

Positive energy emerging from the black hole would be balanced by the negative energy falling in. According to Einstein’s E=mc2 equation, energy is proportional to mass, so negative energy going into a black hole will reduce its mass. Its event horizon would contract, reducing its internal entropy proportionally to the increase in entropy outside. As the black hole contracts it heats up, and gives off more energy, thus contracting quicker and quicker. Finally, it would disappear with an explosion of emissions.

Black holes a few times larger than the sun would be much colder than the general temperature of the universe, so would continue to absorb radiation. Thus black holes will have to wait a long time to emit more energy into the universe than they take in (and in turn contract into nothingness).

Black holes from the early universe would be much smaller though, formed by irregular pressure rather than their own size, and also much hotter. Some would have evaporated already, but some would still be glowing white hot. If humans could harness these early black holes, they could provide immense power. It would be the size of the nucleus of an atom but with the mass of a mountain. One could orbit it round the earth, after towing it through space, but that’s not something scientists can achieve yet.

Scientists can assess background gamma radiation in the universe to calculate how common these early universe black holes are. The evidence suggests they are scarce, so the likelihood of finding and harnessing one is low. What’s more, our technology would not be able to accurately detect one even if it was near Pluto.

If such a black hole were to blow up near Pluto, we could detect it, but the likelihood of that happening right now, given that it takes 20 billion years to reach the point of explosion, is low. To see such an event, we have to look out at around a light-year away. Tell-tale gamma ray bursts indicate a uniform presence of such events throughout, or just outside of, our galaxy. Even if we don’t actually pinpoint these black holes from the early universe, they still tell us a lot about the time they formed. The universe must have been uniform with high pressure for there to be so few black holes from that time.

The theory that black holes emit radiation rubbed people up the wrong way, and was the first significant example of general relativity and quantum theory combining. John G. Taylor opposed Hawking when he announced these discoveries. But in the end, everyone agreed that if these two great theories are right, black holes must radiate.

This new idea about black hole radiation suggests gravitational collapse is not so final after all. Mass or energy lost into a black hole is balanced by its emissions. But is seems when a black hole becomes really small, it will simply disappear. Quantum theory seemed to undermine the idea of singularities, and Hawking’s work turned in that direction in the late 70s, focusing on Feynman’s sum over histories.