{Hawking [(1)]}[19th July 1988]

[Redbook5:210-216][19880719:0000]{Hawking [(1)]}[19th July 1988]

(19880719. )

I have reached p.105* of Stephen Hawking's 'A Brief history of Time',** and have come up against problems. Hawking is an honest and engaging writer; he is describing in non-mathematical language the results of mathematical consideration, which should make the layman hesitate. But some of his conclusions seem very strange.

For example, ***at the beginning of this chapter**** – in which he starts to describe his own more recent work – describing black holes, defined as the set of events from which it is not possible to escape to a large distance: 'It means that the boundary of the black hole, the event horizon, is formed by the light rays that just fail to escape from the black hole, hovering forever just on the edge.... Suddenly I realized that the paths of these light rays could never approach one another. If they did they must eventually run into one another.... {The colliding rays would both} fall into the 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 to be moving parallel to, or away from, 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 it 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 entirely see that if anything within a certain boundary falls into the black hole, that boundary cannot contract – only remain the same, or expand: although the second possibility – expansion – depends upon a non-exclusive meaning of the initial definition,#** contraction depends upon its alteration. What bothers me is Hawking's method of connecting the definition and the conclusion. Is he right to say that 'they could not have been on the boundary'? Or should he say: 'they could not be on the boundary'? A layman would say, if the apparent boundary of something turned out suddenly to be within it, either that he had got the boundary wrong, or that it had moved. And surely, if the decrease of area of the event horizon (and the black hole) would involve formerly parallel (or at least non-mutually-approaching) light rays moving outwards, i.e. away from each other: it is the increase in area which would involve light rays#*** falling into the black hole, either before or after intersecting with each other.#****

*[Ref next entry but one, [Redbook5:210][19880719:0000c]{Hawking [continued (3)]}[19th July 1988]

**([Stephen Hawking, 'A Brief history of Time',] Bantam, 1988)

***Hawking, ibid, 99-100

****[Chapter 7: 'Black Holes Ain’t So Black']

#[My emphasis]

#*BUT [ibid] p107: 'As the black hole loses mass, the area of its event horizon gets smaller....' Have I misunderstood something?

#**[of the black hole, presumably]

#***from the former event horizons

#****Perhaps the boundary alone is meant: i.e. like a 3-d [sic] version of Saturn's rings, its volume expanding or contracting without the volume of the [Black] Hole changing.... But then, why say 'area' not 'volume'?

[continues]

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