General Relativity and the Einstein Equations

Aimed at researchers in mathematics and physics, this monograph, in which the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.

The book is a refreshing exposition of what is not known: The reader will come away feeling that general relativity has many exciting aspects to it just waiting to be discovered.

Klappentext
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 a manifold 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 at researchers 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.


Inhalt
FOREWORD; ACKNOWLEDGEMENTS; 1. Lorentzian Geometry; 2. Special Relativity; 3. General Relativity and the Einstein Equations; 4. Schwarzschild Space-time and Black Holes; 5. Cosmology; 6. Local Cauchy Problem; 7. Constraints; 8. Other Hyperbolic-Elliptic systems; 9. Relativistic Fluids; 10. Kinetic Theory; 11. Progressive Waves; 12. Global Hyperbolicity and Causality; 13. Singularities; 14. Stationary Space-times and Black Holes; 15. Global Existence Theorems, Asymptotically Euclidean Data; 16. Global existence theorems, cosmological case; APPENDICES; I. Sobolev Spaces; II. Elliptic Systems; III. Second Order Quasidiagonal Systems; IV. General Hyperbolic Systems; V. Cauchy Kovalevski and Fuchs theorems; VI. Conformal Methods; VII. Kaluza Klein Formulas

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