Illustrated Theory of Everything: The Origin and Fate of the Universe by Stephen Hawking Read Free Book Online Page B

definition of which points in space-time lay inside a black holeand which lay outside.
I had already discussed with Roger Penrose the idea of defining a black hole asthe set of events from which it was not possible to escape to a large distance.This is now the generally accepted definition. It means that the boundary ofthe black hole, the event horizon, is formed by rays of light that just fail to getaway from the black hole. Instead, they stay forever, hovering on the edge ofthe black hole. It is like running away from the police and managing to keepone step ahead but not being able to get clear away.
Suddenly I realized that the paths of these light rays could not be approachingone another, because if they were, they must eventually run into each other. Itwould be like someone else running away from the police in the opposite direc-tion. You would both be caught or, in this case, fall into a black hole. But ifthese light rays were swallowed up by the black hole, then they could not havebeen on the boundary of the black hole. So light rays in the event horizon hadto be moving parallel to, or away from, each other.
Another way of seeing this is that the event horizon, the boundary of the blackhole, is like the edge of a shadow. It is the edge of the light of escape to a greatdistance, but, equally, it is the edge of the shadow of impending doom. And ifyou look at the shadow cast by a source at a great distance, such as the sun, youwill see that the rays of light on the edge are not approaching each other. Ifthe rays of light that form the event horizon, the boundary of the black hole,can never approach each other, the area of the event horizon could stay thesame or increase with time. It could never decrease, because that would meanthat at least some of the rays of light in the boundary would have to beapproaching each other. In fact, the area would increase whenever matter orradiation fell into the black hole.
Also, suppose two black holes collided and merged together to form a singleblack hole. Then the area of the event horizon of the final black hole wouldbe greater than the sum of the areas of the event horizons of the original blackholes. This nondecreasing property of the event horizon’s area placed animportant restriction on the possible behavior of black holes. I was so excitedwith my discovery that I did not get much sleep that night.The next day I rang up Roger Penrose. He agreed with me. I think, in fact, thathe had been aware of this property of the area. However, he had been using aslightly different definition of a black hole. He had not realized that theboundaries of the black hole according to the two definitions would be thesame, provided the black hole had settled down to a stationary state.
THE SECOND LAW OFTHERMODYNAMICS
The nondecreasing behavior of a black hole’s area was very reminiscent of thebehavior of a physical quantity called entropy, which measures the degree ofdisorder of a system. It is a matter of common experience that disorder willtend to increase if things are left to themselves; one has only to leave a housewithout repairs to see that. One can create order out of disorder-for example,one can paint the house. However, that requires expenditure of energy, and sodecreases the amount of ordered energy available.
A precise statement of this idea is known as the second law of thermodynam-ics. It states that the entropy of an isolated system never decreases with time.Moreover, when two systems are joined together, the entropy of the combinedsystem is greater than the sum of the entropies of the individual systems. Forexample, consider a system of gas molecules in a box. The molecules can bethought of as little billiard balls continually colliding with each other andbouncing off the walls of the box. Suppose that initially the molecules are allconfined to the left-hand side of the box by a partition. If the partition is thenremoved, the molecules will tend to spread out and occupy both halves