The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While the Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.
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"...will surely be extremely useful to researchers already working on cosmic censorship. or contemplating entering the field, and of great interest to classical relativists who are interested in finding out more about it." Robert J. Low, Mathematical Reviews
Book Description
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.
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Inside This Book
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First Sentence:
A singularity, in the sense on which our later definitions will be based, is an exceptional or peculiar point in a space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine parameter length, inextendible curves, incomplete curves, persistent curvature, propagation round, singular boundary points, primordial singularity, causal boundary, global hyperbolicity, mapping norm, genuine singularity, causal curves, cosmic censorship hypothesis, differentiability classes, null infinity, cauchy surface, timelike curves, true singularity, frame bundle, horizontal lift, naked singularities, holonomy group, null geodesics, metric components, strong curvature Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Suppose New!
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A singularity, in the sense on which our later definitions will be based, is an exceptional or peculiar point in a space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine parameter length, inextendible curves, incomplete curves, persistent curvature, propagation round, singular boundary points, primordial singularity, causal boundary, global hyperbolicity, mapping norm, genuine singularity, causal curves, cosmic censorship hypothesis, differentiability classes, null infinity, cauchy surface, timelike curves, true singularity, frame bundle, horizontal lift, naked singularities, holonomy group, null geodesics, metric components, strong curvature Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
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22
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cite this book:
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- Modern Cosmology and the Dark Matter Problem (Cambridge Lecture Notes in Physics) by D. W. Sciama in Front Matter
- Categories, Bundles and Spacetime Topology (Mathematics and Its Applications (closed)) by C.T. Dodson in Back Matter
- Modern Cosmology (Cambridge Science Classics) by D. W. Sciama in Front Matter
- Sobolev spaces, Volume 65 (Pure and Applied Mathematics) by Author Unknown in Back Matter
- Black Hole Uniqueness Theorems (Cambridge Lecture Notes in Physics) by Markus Heusler in Front Matter, and Back Matter
- Dismantling the Big Bang by Alex Williams on page 97, and page 98
- Is the Universe Open or Closed?: The Density of Matter in the Universe (Cambridge Lecture Notes in Physics) by Peter Coles in Front Matter
- Lattice Models of Polymers (Cambridge Lecture Notes in Physics) by Carlo Vanderzande in Front Matter
- Global Lorentzian Geometry (Chapman & Hall/CRC Pure and Applied Mathematics) by John K. Beem in Back Matter
See all 22 books citing this book
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