广义相对论是描述物质间引力相互作用的理论，其基础由爱因斯坦于1915年完成，1916年正式发表，这一理论抢先发售把引力场解释成时空的弯曲。本书从对狭义相对论和张量的回顾开始，扩展到广义相对论的基本要素以及广义相对论在光的引力偏转、优选定位系统、黑洞、引力波和宇宙学中的应用。编写本书的目的是使读者对基本的物理概念有很好的理解，培养一种可以欣赏并在许多情况下推导出相关理论的重要应用的能力，为希望在该领域进行进一步研究的读者打下坚实的基础。本书适合物理及相关专业师生使用，也适合物理爱好者参考阅读。

Preface
About the author
List of symbols
1 Concepts in spe relativity
1.1 Galilean relativity
1.2 Inertial frames
1.3 Spe relativity
1.4 Velocity addition, length contraction, and time dilation
1.5 Questions
References
2 Tensors in relativity
2.1 Motivation
2.2 General tensors and their basic properties
2.3 Lorentz tensors
2.4 Example: 4-momentum and force
2.5 Example: Doppler effect
2.6 Questions
Reference
3 The equivalence principle and local inertial frames
3.1 Inertial versus gravitational mass
3.2 Einstein's equivalence principle
3.3 Local inertial frames
3.4 Questions
References
4 The motion of freely falling particles in general relativity
4.1 Local inertial frames and the geodesic equation
4.2 The metric tensor
4.3 Gravity as geometry
4.4 The Newtonian limit
4.5 Questions
5 The Schwarzschild metric and black holes
5.1 Spherical symmetry and the Schwarzschild metric
5.2 Geodesics in spherically symmetric spacetimes
5.3 Particle geodesics in a Schwarzschild spacetime
5.4 Deflection of light by the Sun
5.5 Falling into a black hole
5.6 Questions
References
6 Tensors and geometry
6.1 Covariant derivatives
6.2 Basic properties of covariant derivatives
6.3 Riemann and Ricci tensors
6.4 Symmetries and Bianchi identities
6.5 Questions
Reference
7 Einstein's field equations
7.1 Overview
7.2 Energy-momentum tensor and conservation laws
7.2.1 Conservation of electric charge
7.2.2 Conservation of energy-momentum
7.2.3 The energy-momentum tensor
7.3 The field equations for general relativity
7.4 The cosmological constant
7.5 Questions
References
8 Solving the field equations: vacuum solutions
8.1 The vacuum field equations
8.2 The Schwarzschild-de Sitter solution
8.2.1 Vacuum field equations for static spherically symmetric
metrics
8.2.2 Deriving the Schwarzschild-de Sitter metric
8.3 Gravitational waves
8.3.1 Weak-field approximation
8.3.2 Harmonic gauge
8.3.3 Plane waves and polarisation
8.3.4 Detection of gravitational waves
8.4 Questions
References
9 Solving the field equations: cosmological solutions
9.1 The cosmological principle
9.2 The Friedmann-Robertson-Walker metric
9.2.1 Checking homogeneity and isotropy
9.2.2 Galaxies, distances, and the cosmological redshift
9.3 Friedmann-Robertson-Walker universes
9.3.1 A perfect (fluid) world
9.3.2 Local conservation of energy and momentum
9.3.3 Cosmic microwave background
9.3.4 Our accelerating Universe
9.4 Questions
References
Appendices
A Derivation of Lorentz transformations
B Derivation of Einstein's field equations
C Remarks on selected questions
编辑手记