Illustrated Theory of Everything: The Origin and Fate of the Universe Read Online Free PDF Page A

universe whichwere roughly like Friedmann’s models but which took account of the irregular-ities and random velocities of galaxies in the real universe. They showed thatsuch models could start with a big bang, even though the galaxies were nolonger always moving directly away from each other. But they claimed thatthis was still only possible in certain exceptional models in which the galaxieswere all moving in just the right way. They argued that since there seemed tobe infinitely more Friedmann-like models without a big bang singularity thanthere were with one, we should conclude that it was very unlikely that therehad been a big bang. They later realized, however, that there was a much moregeneral class of Friedmann-like models which did have singularities, and inwhich the galaxies did not have to be moving in any special way. They there-fore withdrew their claim in 1970.
The work of Lifshitz and Khalatnikov was valuable because it showed that theuniverse could have had a singularity-a big bang-if the general theory of rel-ativity was correct. However, it did not resolve the crucial question: Does gen-eral relativity predict that our universe should have the big bang, a beginningof time? The answer to this came out of a completely different approach start-ed by a British physicist, Roger Penrose, in 1965. He used the way light conesbehave in general relativity, and the fact that gravity is always attractive, toshow that a star that collapses under its own gravity is trapped in a region whoseboundary eventually shrinks to zero size. This means that all the matter in thestar will be compressed into a region of zero volume, so the density of matterand the curvature of space-time become infinite. In other words, one has a sin-gularity contained within a region of space-time known as a black hole.
At first sight, Penrose’s result didn’t have anything to say about the questionof whether there was a big bang singularity in the past. However, at the timethat Penrose produced his theorem, I was a research student desperately look-ing for a problem with which to complete my Ph.D. thesis. I realized that if onereversed the direction of time in Penrose’s theorem so that the collapse becamean expansion, the conditions of his theorem would still hold, provided theuniverse were roughly like a Friedmann model on large scales at the presenttime. Penrose’s theorem had shown that any collapsing star must end in asingularity; the time-reversed argument showed that any Friedmann-likeexpanding universe must have begun with a singularity. For technical reasons,Penrose’s theorem required that the universe be infinite in space. So I coulduse it to prove that there should be a singularity only if the universe wasexpanding fast enough to avoid collapsing again, because only that Friedmannmodel was infinite in space.
During the next few years I developed new mathematical techniques toremove this and other technical conditions from the theorems that provedthat singularities must occur. The final result was a joint paper by Penroseand myself in 1970, which proved that there must have been a big bang singu-larity provided only that general relativity is correct and that the universecontains as much matter as we observe.
There was a lot of opposition to our work, partly from the Russians, whofollowed the party line laid down by Lifshitz and Khalatnikov, and partly frompeople who felt that the whole idea of singularities was repugnant and spoiledthe beauty of Einstein’s theory. However, one cannot really argue with themathematical theorem. So it is now generally accepted that the universe musthave a beginning.

The Theory of Everything: The Origin and Fate of the Universe

Chapter 3 - THIRD LECTURE - BLACK HOLES
The term black hole is of very recent origin. It was coined in 1969 by theAmerican scientist John Wheeler as a graphic description of an idea thatgoes back at least two hundred years. At that time there were two theoriesabout light.