| Description |
1 online resource (xx, 279 pages) |
| Contents |
I. Riemannian and Lorentzian geometry -- I.1. Introduction -- I.2. Differentiable manifolds and mappings -- I.2.1. Differentiable manifolds -- I.2.2. Differentiable mappings -- I.2.3. Submanifolds -- I.2.4. Tangent and cotangent spaces -- I.2.5. Vector fields and 1-forms -- I.2.6. Moving frames -- I.3. Tensors and tensor fields -- I.3.1. Tensors, products and contraction -- I.3.2. Tensor fields. Pullback and Lie derivative -- I.3.3. Exterior forms -- I.4. Structure coefficients of moving frames -- I.5. Pseudo-Riemannian metrics -- I.5.1. General properties -- I.5.2. Riemannian metrics -- I.5.3. Lorentzian metrics -- I.6. Causality -- I.6.1. Causal and null cones -- I.6.2. Future and past -- I.6.3. Spacelike submanifolds -- I.6.4. Length and geodesics -- I.7. Connections -- I.7.1. Linear connection -- I.7.2. Riemannian connection -- I.8. Geodesics, another definition -- I.8.1. Pseudo-Riemannian manifolds -- I.8.2. Riemannian manifolds -- I.8.3. Lorentzian manifolds |
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VIII. 4. Preservation of the wave gauges -- VIII. 4.1. Wave gauge constraints -- VIII. 5. Local existence and uniqueness -- VIII. 6. Solution of the wave gauge constraints -- VIII. 6.1. Asymptotically Euclidean manifolds -- VIII. 6.2.Compact manifolds -- VIII. 7. Geometric n 1 splitting -- VIII. 7.1. Adapted frame and coframe -- VIII. 7.2. Dynamical system with constraints for g and K -- VIII. 7.3. Geometric Cauchy problem. Regularity assumptions -- VIII. 8. Solution of the constraints by the conformal method -- VIII. 8.1. Conformally formulated (CF) constraints -- VIII. 8.2. Elliptic system -- VIII. 8.3. Physical comment -- VIII. 9. Motion of a system of compact bodies -- VIII. 9.1. Effective one-body (EOB) method -- VIII. 9.2. Numerical Relativity -- VIII. 10. Global properties -- VIII. 10.1. Global hyperbolicity and global uniqueness -- VIII. 10.2. Global existence -- VIII. 11. Singularities and cosmic censorship conjectures -- VIII. 11.1. Strong cosmic censorship conjecture |
| Summary |
General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
General relativity (Physics)
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Black holes (Astronomy)
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Gravitational waves.
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Cosmology.
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cosmology.
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SCIENCE -- Energy.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Physics -- General.
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Black holes (Astronomy)
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Cosmology
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General relativity (Physics)
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Gravitational waves
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| Form |
Electronic book
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| ISBN |
9780191644528 |
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0191644528 |
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