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9780199230723

General Relativity and the Einstein Equations

by
  • ISBN13:

    9780199230723

  • ISBN10:

    0199230722

  • Format: Hardcover
  • Copyright: 2009-02-04
  • Publisher: Oxford University Press

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Summary

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.

Table of Contents

Foreword
Acknowledgements
Lorentzian Geometry
Special Relativity
General Relativity and the Einstein Equations
Schwarzschild Space-time and Black Holes
Cosmology
Local Cauchy Problem
Constraints
Other Hyperbolic-Elliptic systems
Relativistic Fluids
Kinetic Theory
Progressive Waves
Global Hyperbolicity and Causality
Singularities
Stationary Space-times and Black Holes
Global Existence Theorems, Asymptotically Euclidean Data
Global existence theorems, cosmological case
Appendices
Sobolev Spaces
Elliptic Systems
Second Order Quasidiagonal Systems
General Hyperbolic Systems
Cauchy Kovalevski and Fuchs theorems
Conformal Methods
Kaluza Klein Formulas
Table of Contents provided by Publisher. All Rights Reserved.

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