General Relativity and the Einstein Equations

Hardcover | October 1, 2008

byYvonne Choquet-bruhat

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General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with amanifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed atresearchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.

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General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with amanifold of dimensions possibly greater tha...

Yvonne Choquet-Bruhat is a Membre de l'Academie des Sciences in Paris.

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Hardcover

$113.14 online$135.50list price(save 16%)
Format:HardcoverDimensions:350 pagesPublished:October 1, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199230722

ISBN - 13:9780199230723

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Table of Contents

ForewordAcknowledgements1. Lorentzian Geometry2. Special Relativity3. General Relativity and the Einstein Equations4. Schwarzschild Space-time and Black Holes5. Cosmology6. Local Cauchy Problem7. Constraints8. Other Hyperbolic-Elliptic systems9. Relativistic Fluids10. Kinetic Theory11. Progressive Waves12. Global Hyperbolicity and Causality13. Singularities14. Stationary Space-times and Black Holes15. Global Existence Theorems, Asymptotically Euclidean Data16. Global existence theorems, cosmological caseAppendicesI. Sobolev SpacesII. Elliptic SystemsIII. Second Order Quasidiagonal SystemsIV. General Hyperbolic SystemsV. Cauchy Kovalevski and Fuchs theoremsVI. Conformal MethodsVII. Kaluza Klein Formulas