Preface
Notation and Conventions
PART I. FUNDAMENTALS
1. Introduction
1.1 Introduction
1.2 Space and Time in Prerelativity Physics and in Special Relativity
1.3 The Spacetime Metric
1.4 General Relativity
2. Manifolds and Tensor Fields
2.1 Manifolds
2.2 Vectors
2.3 Tensors; the Metric Tensor
2.4 The Abstract Index Notation
3. Curvature
3.1 Derivative Operators and Parallel Transport
3.2 Curvature
3.3 Geodesics
3.4 Methods for Computing Curvature
4. Einstein’s Equation
4.1 The Geometry of Space in Prerelativity Physics; General and Special Covariance
4.2 Special Relativity
4.3 General Relativity
4.4 Linearized Gravity: The Newtonian Limit and Gravitational Radiation
5. Homogeneous, Isotropic Cosmology
5.1 Homogeneity and Isotrophy
5.2 Dynamics of a Homogeneous, Isotropic Universe
5.3 The Cosmological Redshift; Horizons
5.4 The Evolution of Our Universe
6. The Schwartzschild Solution
6.1 Derivation of the Schwartzschild Solution
6.2 Interior Solutions
6.3 Geodesics of Schwartzschild: Gravitation Redshift, Perihelion Precession, Bending of Light, and Time Delay
6.4 The Kruskal Extension
PART II. ADVANCED TOPICS
7. Methods for Solving Einstein’s Equation
7.1 Stationary, Axisymmetric Solutions
7.2 Spatially Homogeneous Cosmologies
7.3 Algebraically Special Solutions
7.4 Methods for Generating Solutions
7.5 Perturbations
8. Casual Structure
8.1 Futures and Pasts: Basic Definitions and Results
8.2 Causality Conditions
8.3 Domains of Dependence; Global Hyperbolicity
9. Singularities
9.1 What is a Singularity?
9.2 Timelike and Null Geodesic Congruences
9.3 Conjugate Points
9.4 Existence of Maximum Length Curves
9.5 Singularity Theorems
10. The Initial Value Formulation
10.1 Initial Value Formulation for Particles and Fields
10.2 Initial Value Formulation of General Relativity
11. Asymptotic Flatness
11.1 Conformal Infinity
11.2 Energy
12. Black Holes
12.1 Black Holes and the Cosmic Censor Conjecture
12.2 General Properties of Black Holes
12.3 The Charged Kerr Black Holes
12.4 Energy Extraction from Black Holes
12.5 Black Holes and Thermodynamics
13. Spinors
13.1 Spinors in Minkowski Spacetime
13.2 Spinors in Curved Spacetime
14. Quantum Effects in Strong Gravitational Fields
14.1 Quantum Gravity
14.2 Quantum Fields in Curved Spacetime
14.3 Particle Creation near Black Holes
14.4 Black Hold Thermodynamics
APPENDICES
A. Topological Spaces
B. Differential Forms, Integration, and Frobenius’s Theorem
B.1 Differential Forms
B.2 Integration
B.3 Frobenius’s Theorem
C. Maps of Manifolds, Lie Derivatives, and Killing Fields
C.1 Maps of Manifolds
C.2 Lie Derivatives
C.3 Killing Vector Fields
D. Conformal Transformations
E. Lagrangian and Hamiltonian Formulations of Einstein’s Equation
E.1 Lagrangian Formulation
E.2 Hamiltonian Formulation
F. Units and Dimensions
References
Index
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1 有用 自由度 2019-08-04 11:41:19
真是一本名著啊,不得不承认难度还是很大的,在400多页的篇幅cover到这么多内容,学习的时候要结合梁书的注解和一些文献才能全部读完,真是不容易啊。场论有peskin,gr有wald!
0 有用 DE 2022-10-14 23:48:12 上海
清澈
1 有用 阅微草堂 2016-05-01 03:01:51
爱因斯坦场方程包含了所有的动力学,经典力学的拉格朗日仅仅是路径上的,而场方程的则是在流形上的
2 有用 长安绿秋 2017-08-28 14:48:13
这本书的精华就在于厚重的数学推导啊!第八章到十四章是别的GR书很少提的东西,对四种horizon的精准定义,5个版本的singularity定理,面积不减定理的证明,黑洞热力学,宇宙监督原理三种表述,Hawking温度的非trivial推导,数学上此书真的无敌!
0 有用 狂夜舞者 2017-04-19 08:59:17
Another good book - but this book take quite some time to get used to the formulism here.
0 有用 DE 2022-10-14 23:48:12 上海
清澈
0 有用 Photon 2022-07-15 22:20:15
速读,涵盖面非常广,信息密度大,初学可能会很辛苦。很多topic都覆盖了,包括奇点定理,因果结构,甚至spinor。不愧是经典教材,但感觉更适合学完一遍按需查找的工具书。
0 有用 huyan00 2020-06-13 10:50:47
看得兴奋
0 有用 ZsxMath 2019-12-09 04:46:38
Hawking&Ellis的简略版本。
1 有用 自由度 2019-08-04 11:41:19
真是一本名著啊,不得不承认难度还是很大的,在400多页的篇幅cover到这么多内容,学习的时候要结合梁书的注解和一些文献才能全部读完,真是不容易啊。场论有peskin,gr有wald!