The Large Scale Structure of Space Time

Author: S. W. Hawking
Publisher: Cambridge University Press
ISBN: 1139810952
Format: PDF, Docs
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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.

The Large Scale Structure of Space Time

Author: S. W. Hawking
Publisher: Cambridge University Press
ISBN: 9780521099066
Format: PDF, Kindle
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This 1973 book discusses Einstein's General Theory of Relativity and its predictions concerning black holes and singularities in space-time itself.

The Large Scale Structure of Space Time

Author: Stephen W. Hawking
Publisher:
ISBN: 9781139811446
Format: PDF
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This 1973 book discusses Einstein's General Theory of Relativity and its predictions concerning black holes and singularities in space-time itself.

Advanced General Relativity

Author: John Stewart
Publisher: Cambridge University Press
ISBN: 9780521449465
Format: PDF, ePub, Mobi
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A self-contained introduction to advanced general relativity.

Spacetime and Singularities

Author: Gregory L. Naber
Publisher: Cambridge University Press
ISBN: 9780521336123
Format: PDF, Docs
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Naber provides an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of space-time and that play a role in the Penrose-Hawking singularity theorems. The author's primary purpose is to give a rigorous proof of the simplest of these theorems, by the one that is representative of the whole. He provides exercises and examples at the end of each chapter. No previous exposure either to relativity theory of differential geometry is required of the reader, as necessary concepts are developed when needed, though some restrictions ae imposed on the types of space considered.

The Analysis of Space Time Singularities

Author: C. J. S. Clarke
Publisher: Cambridge University Press
ISBN: 9780521437967
Format: PDF, ePub
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The different possible singularities are defined and the mathematical methods needed to extend the space-time are described in detail in this book. Results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor.

Exact Space Times in Einstein s General Relativity

Author: Jerry B. Griffiths
Publisher: Cambridge University Press
ISBN: 1139481169
Format: PDF, ePub, Mobi
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Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.

Exact Solutions of Einstein s Field Equations

Author: Hans Stephani
Publisher: Cambridge University Press
ISBN: 9781139435024
Format: PDF
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A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.

Supermanifolds

Author: Bryce DeWitt
Publisher: Cambridge University Press
ISBN: 9780521423779
Format: PDF, ePub, Docs
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This updated and expanded second edition of an established text presents a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the superanalogs of all the basic structures of ordinary manifold theory.

Spinors and Space Time Volume 1 Two Spinor Calculus and Relativistic Fields

Author: Roger Penrose
Publisher: Cambridge University Press
ISBN: 9780521337076
Format: PDF, ePub, Mobi
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This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.