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General Relativity and the Einstein Equations
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 CauchyExpand
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Analysis, manifolds, and physics
Contents. Preface. Preface to the second edition. Preface. Contents. Conventions. I. Review of fundamental notions of analysis. II. Differential calculus on banach spaces. III. DifferentiableExpand
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Future Global in Time Einsteinian Spacetimes with U(1) Isometry Group
Abstract. We prove that spacetimes satisfying the vacuum Einstein equations on a manifold of the form¶ $ \Sigma \times U(1) \times R $ where $ \Sigma $ is a compact surface of genus G > 1 and whereExpand
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Einstein constraints on asymptotically Euclidean manifolds
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifoldsExpand
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The Cauchy Problem on a Characteristic Cone for the Einstein Equations in Arbitrary Dimensions
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary space–time dimensions n + 1 ≥ 3. We solve these constraints and show that theyExpand
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Global Wave Maps on Robertson–Walker Spacetimes
We prove the global existence and uniqueness of wave maps onexpanding universes of dimension three or four, that is Robertson–Walkerspacetimes whose inverse radius is integrable with respect to theExpand
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On the stability of flat space
Abstract It is shown that: (1) there exists, near flat space, a neighborhood of nonsingular asymptotically flat weak field solutions of the initial value equations of General Relativity; theExpand
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