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Introduction to general relativity, black holes, and cosmology /
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 int...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
2015.
|
| Edición: | First edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.