The Large Scale Structure of Space-Time

Front Cover
Cambridge University Press, 1973 - Science - 391 pages
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
 

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Contents

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XXXIV
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Page 189 - However the existence of such curves would seem to lead to the possibility of logical paradoxes: for, one could imagine that with a suitable rocketship one could travel round such a curve and, arriving back before one's departure, one could prevent oneself from setting out in the first place. Of course there is a contradiction only if one assumes a simple notion of free will; but this is not something which can be dropped lightly since the whole of our philosophy of science is based on the assumption...
Page 365 - Mitchell's work, made a similar prediction: "the attractive force of a heavenly body could be so large that light could not flow out of it.
Page 350 - ... interest in a collection of ideas, known as the Anthropic Cosmological Principle, which offer a means of relating Mind and observership directly to the phenomena traditionally within the encompass of physical science. The expulsion of Man from his self-assumed position at the centre of Nature owes much to the Copernican principle that we do not occupy a privileged position in the Universe. This Copernican assumption would be regarded as axiomatic at the outset of most scientific investigations....
Page 364 - Some slars have suddenly appeared, and then disappeared, after having shone for several months with the most brilliant splendour. Such was the star observed by Tycho Brahe in the year 1572, in the constellation Cassiopeia. In a short time it surpassed the most brilliant stars, and even Jupiter itself. Its light then waned away, and finally disappeared sixteen months after its discovery. Its colour underwent several changes...
Page 364 - Therefore there exists, in the immensity of space, opaque bodies as considerable in magnitude, and perhaps equally as numerous as the stars.
Page 271 - THEOREM 2. <Jl cannot be timelike and null geodesically complete if: (1) The energy-momentum tensor obeys the same inequality as in theorem 1. (2) Strong causality holds on (p), the closure of the past of some point p. (3) There is a past directed unit timelike vector (i)aatp and a positive constant b such that, if v°...

About the author (1973)

Stephen William Hawking was born in Oxford, England on January 8, 1942. He received a first class honors degree in natural science from Oxford University and a Ph.D. from Cambridge University. He was a theoretical physicist and has held the post of Lucasian Professor of Mathematics at Cambridge University from 1982 until his death. In 1974, he was elected a Fellow of the Royal Society, the world's oldest scientific organization. In 1963, he learned he had amyotrophic lateral sclerosis, a neuromuscular wasting disease also known as Lou Gehrig's disease. The disease confined him to a wheelchair and reduced his bodily control to the flexing of a finger and voluntary eye movements, but left his mental faculties untouched. He became a leader in exploring gravity and the properties of black holes. He wrote numerous books including A Brief History of Time: From the Big Bang to Black Holes, Black Holes and Baby Universes, On the Shoulders of Giants, A Briefer History of Time, The Universe in a Nutshell, The Grand Design, and Brief Answers to the Big Questions. In 1982, he was named a commander of the British Empire. A film about his life, The Theory of Everything, was released in 2014 and was based on his first wife Jane Hawking's book Traveling to Infinity: My Life with Stephen. He died on March 14, 2018 at the age of 76.

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