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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achronal affine parameter asymptotically basis black hole boundary canbe Cauchy development Cauchy surface causality closed trapped surface collapse compact components condition conjugate constant contained converge coordinate neighbourhoods covariant derivatives curvature defined density diffeomorphism differential Einstein equations endpoint energy energy–momentum tensor ergosphere event horizon field equations figure finite function future futuredirected geodesic curve geodesically complete gravitational Hausdorff Image inextendible infinity intersect inthe isometry J+(p Kerr solution Killing vector lemma Lie derivative Lorentz metric manifold Minkowski Minkowski space nonspacelike curve nonzero null geodesic ofthe onecan open set particle past pastdirected Penrose Penrose diagram point q proposition region respect Robertson–Walker satisfied scalar Schwarzschild shows singularity space space–time spacelike surface spherically symmetric tangent vector thatthe theorem timelike curve timelike geodesics topology twosphere twosurface vanishes vector field worldline zero