Introduction to general relativity, black holes, and cosmology / / Yvonne Choquet-Bruhat ; with a foreword by Thibault Damour.

• Superior document: Oxford scholarship online
• VerfasserIn: Choquet-Bruhat, Yvonne,
• Place / Publishing House: Oxford : : Oxford University Press,, 2023.
• Year of Publication: 2023
• Edition: First edition.
• Language: English
• Series: Oxford scholarship online.
• Physical Description: 1 online resource (301 pages)
• Notes: This edition also issued in print: 2023.

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 physics knowledge is required.

Table of Contents

Cover; Foreword; Preface; Notation; Contents; Part A Fundamentals; 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 metricsI.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; I.9 Curvature; I.9.1 Definitions; I.9.2 Symmetries and antisymmetries; I.9.3 Differential Bianchi identity and contractions; I.10 Geodesic deviation; I.11 Linearized Ricci tensor; I.11.1 Linearized Bianchi identities

I.12 Physical commentI.13 Solutions of selected exercises; I.14 Problems; I.14.1 Liouville theorem; I.14.2 Codifferential δ and Laplacian of an exterior form; I.14.3 Geodesic normal coordinates; I.14.4 Cases d=1, 2, and 3; I.14.5 Wave equation satisfied by the Riemann tensor; I.14.6 The Bel-Robinson tensor; I.14.7 The Weyl tensor; I.14.8 The Cotton-York tensor; I.14.9 Linearization of the Riemann tensor; I.14.10 Second derivative of the Ricci tensor; II Special relativity; II.1 Introduction; II.2 Newtonian mechanics; II.2.1 The Galileo-Newton Spacetime

II.2.2 Newtonian dynamics. Galileo groupII.2.3 Physical comment; II.2.4 The Maxwell equations in Galileo-Newton spacetime; II.3 The Lorentz and Poincaré groups; II.4 Lorentz contraction and dilation; II.5 Electromagnetic field and Maxwell equations in Minkowski spacetime M4; II.6 Maxwell equations in arbitrary dimensions; II.7 Special Relativity; II.7.1 Proper time; II.7.2 Proper frame and relative velocities; II.8 Some physical comments; II.9 Dynamics of a pointlike mass; II.9.1 Newtonian law; II.9.2 Relativistic law; II.9.3 Newtonian approximation of the relativistic equation

II.9.4 Equivalence of mass and energyII.9.5 Particles with zero rest mass; II.10 Continuous matter; II.10.1 Case of dust (incoherent matter), massive particles; II.10.2 Perfect fluids; II.10.3 Yang-Mills fields; II.11 Problems; II.11.1 Lorentz transformation of the Maxwell equations; II.11.2 The relativistic Doppler-Fizeau effect; III General Relativity; III.1 Introduction; III.2 Principle of general covariance; III.3 The Galileo-Newton equivalence principle; III.4 General Relativity; III.4.1 Einstein equivalence principles; III.4.2 Conclusion; III.5 Constants and units of measurement

III.6 Classical fields in General Relativity