In Hawking's famous publication "A Brief History of Time", he discusses the steps leading to his discovery of Hawking Radiation. He first argues that due to the aforementioned feature of light at the edge of the event horizon, the area of the event horizon is non-decreasing. He then goes on to say that black holes appear to violate the Second Law of Thermodynamics since you can throw particles in a black hole decreasing entropy outside the black hole. Therefore it was proposed that the area of the event horizon would be proportional to the entropy of the black hole allowing it to conform with the Second Law. This led him to deduce that black holes must have temperature and thus must emit radiation.
Unfortunately I have had difficulty grasping the first step in this sequence - i.e. how Hawking initially postulated that black holes have non-decreasing area. His exact words are:
"Suddenly I realised that the paths of these light rays could never approach one another. If they did, they must eventually run into one another. It would be like meeting someone else running away from the police in the opposite direction - you would both be caught! (Or, in this case, fall into a black hole.) But if these light rays were swallowed up by the black hole, then they could not have been on the boundary of the black hole. So the paths of light rays in the event horizon had always be moving parallel to, or away from, each other. Another way of seeing this is that the event horizon, the boundary of the black hole, is like the edge of a shadow - the shadow of impending doom. If you look at the shadow cast by a source at a great distance, such as the sun, you will see that the rays of light in the edge are not approaching each other.
If the 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 might stay the same or increase with time but if could never decrease because that would mean that at least some of the rays of light in the boundary would have to be approaching each other.
I guess the root of my difficulty here is my interpretation of the edge of the event horizon. I thought it was essentially the surface of a sphere or ellipsoid whereby matter has to travel at the speed of light in order to escape. I can't seem to fit in the ideas of "parallel" and "approaching each other" in the context of the edge of the event horizon.
I know I could be missing something really obvious here but any help appreciated!