The Large Scale Structure of Space-TimeEinstein'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
XXXIV | 189 |
XXXV | 201 |
XXXVI | 206 |
XXXVII | 213 |
XXXVIII | 217 |
XXXIX | 221 |
XL | 226 |
XLI | 227 |
XLII | 228 |
XLIII | 231 |
XLIV | 233 |
XLV | 244 |
XLVI | 249 |
XLVII | 254 |
XLVIII | 256 |
XLIX | 261 |
L | 276 |
LI | 284 |
LII | 289 |
LIII | 299 |
LV | 308 |
LVI | 323 |
LVII | 348 |
LIX | 359 |
LX | 365 |
LXI | 369 |
LXIII | 373 |
LXIV | 381 |
LXV | 385 |
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Common terms and phrases
asymptotically basis body boundary Cauchy surface causality closed collapse compact complete components condition cone connection consider constant contained continuous converge coordinates corresponding covering curvature defined definition density derivatives determined differential direction distance Einstein empty endpoint energy equal equations event horizon example existence expressed extended fact figure finite follows function future give given holds implies incomplete infinity initial integral intersect lemma length light limit lines Lorentz metric manifold mass matter measure metric g negative neighbourhood non-spacelike curve normal null geodesic observer obtain orthogonal parameter particle past positive predictable properties proposition regard region relation represents respect result satisfied Schwarzschild similar singularity solution space space-time spacelike star Suppose surface symmetric takes tangent vector tensor theorem timelike curve topology unique universe values vanishes variation vector field zero
Popular passages
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°...
References to this book
Nonlinear Functional Analysis and Its Applications: Part 2 B: Nonlinear ... E. Zeidler No preview available - 1989 |
Manifolds, Tensor Analysis, and Applications Ralph Abraham,J.E. Marsden,Tudor Ratiu Limited preview - 1993 |

