Chapter
3.5 Causality, and velocities larger than that of light
4 Mechanics of Special Relativity
5.1 Invariance of phase and null vectors
5.2 The Doppler effect – shift in the frequency of a wave
5.3 Aberration – change in the direction of a light ray
5.4 The visual shape of moving bodies
5.5 Reflection at a moving mirror
5.6 Dragging of light within a fluid
6 Four-dimensional vectors and tensors
6.3 Symmetries of tensors
6.4 Algebraic properties of second rank tensors
7 Electrodynamics in vacuo
7.1 The Maxwell equations in three-dimensional notation
7.2 Current four-vector, four-potential, and the retarded potentials
7.3 Field tensor and the Maxwell equations
7.4 Poynting’s theorem, Lorentz force, and the energy-momentum tensor
7.5 The variational principle for the Maxwell equations
8 Transformation properties of electromagnetic fields: examples
8.1 Current and four-potential
8.2 Field tensor and energy-momentum tensor
9 Null vectors and the algebraic properties of electromagnetic field tensors
9.1 Null tetrads and Lorentz transformations
9.2 Self-dual bivectors and the electromagnetic field tensor
9.3 The algebraic classification of electromagnetic fields
9.4 The physical interpretation of electromagnetic null fields
10 Charged point particles and their field
10.1 The equations of motion of charged test particles
10.2 The variational principle for charged particles
10.4 The field of a charged particle in arbitrary motion
10.5 The equations of motion of charged particles – the self-force
Further reading for Chapter 10
11 Pole-dipole particles and their field
11.2 The dipole term and its field
11.3 The force exerted on moving dipoles
12 Electrodynamics in media
12.1 Field equations and constitutive relations
12.2 Remarks on the matching conditions at moving surfaces
12.3 The energy-momentum tensor
13 Perfect fluids and other physical theories
13.2 Other physical theories – an outlook
14 Introduction: the force-free motion of particles in Newtonian mechanics
14.3 The geodesic equation
15 Why Riemannian geometry?
16.2 Geodesics and Christoffel symbols
16.3 Coordinate transformations
16.4 Special coordinate systems
16.5 The physical meaning and interpretation of coordinate systems
Further reading for Chapter 16
17.2 Tensors and other geometrical objects
17.3 Algebraic operations with tensors
17.4 Tetrad and spinor components of tensors
Further reading for Section 17.4
18 The covariant derivative and parallel transport
18.1 Partial and covariant derivatives
18.2 The covariant differential and local parallelism
18.3 Parallel displacement along a curve and the parallel propagator
18.4 Fermi–Walker transport
Further reading for Chapter 18
19.1 Intrinsic geometry and curvature
19.2 The curvature tensor and global parallelism of vectors
19.3 The curvature tensor and second derivatives of the metric tensor
19.4 Properties of the curvature tensor
19.5 Spaces of constant curvature
Further reading for Chapter 19
20 Differential operators, integrals and integral laws
20.2 Some important differential operators
20.3 Volume, surface and line integrals
20.5 Integral conservation laws
Further reading for Chapter 20
21 Fundamental laws of physics in Riemannian spaces
21.1 How does one find the fundamental physical laws?
21.3 Electrodynamics in vacuo
21.6 Perfect fluids and dust
21.7 Other fundamental physical laws
Further reading for Chapter 21
III. Foundations of Einstein’s theory of gravitation
22 The fundamental equations of Einstein’s theory of gravitation
22.1 The Einstein field equations
22.3 The equations of motion of test particles
Further reading for Section 22.3
22.4 A variational principle for Einstein’s theory
23 The Schwarzschild solution
23.2 The solution of the vacuum field equations
23.3 General discussion of the Schwarzschild solution
23.4 The motion of the planets and perihelion precession
23.5 The propagation of light in the Schwarzschild field
23.6 Further aspects of the Schwarzschild solution
23.7 The Reissner–Nordström solution
24 Experiments to verify the Schwarzschild metric
24.1 Some general remarks
24.2 Perihelion precession and planetary orbits
24.3 Light deflection by the Sun
24.5 Measurements of the travel time of radar signals (time delay)
24.6 Geodesic precession of a top
Further reading for Chapter 24
25.1 The spherically symmetric gravitational lens
25.2 Galaxies as gravitational lenses
26 The interior Schwarzschild solution
26.2 The solution of the field equations
26.3 Matching conditions and connection to the exterior Schwarzschild solution
26.4 A discussion of the interior Schwarzschild solution
IV. Linearized theory of gravitation, far fields and gravitational waves
27 The linearized Einstein theory of gravity
27.1 Justification for a linearized theory and its realm of validity
27.2 The fundamental equations of the linearized theory
27.3 A discussion of the fundamental equations and a comparison with special-relativistic electrodynamics
27.4 The far field due to a time-dependent source
27.5 Discussion of the properties of the far field (linearized theory)
27.6 Some remarks on approximation schemes
Further reading for Section 27.6
28 Far fields due to arbitrary matter distributions and balance equations for momentum and angular momentum
28.1 What are far fields?
28.2 The energy-momentum pseudotensor for the gravitational field
28.3 The balance equations for momentum and angular momentum
28.4 Is there an energy law for the gravitational field?
Further reading for Chapter 28
29.1 Are there gravitational waves?
29.2 Plane gravitational waves in the linearized theory
29.3 Plane waves as exact solutions of Einstein’s equations
29.4 The experimental evidence for gravitational waves
30 The Cauchy problem for the Einstein field equations
30.2 Three-dimensional hypersurfaces and reduction formulae for the curvature tensor
30.3 The Cauchy problem for the vacuum field equations
30.4 The characteristic initial value problem
30.5 Matching conditions at the boundary surface of two metrics
V. Invariant characterization of exact solutions
31 Preferred vector fields and their properties
31.1 Special simple vector fields
31.2 Timelike vector fields
32 The Petrov classification
32.1 What is the Petrov classification?
32.2 The algebraic classification of gravitational fields
32.3 The physical interpretation of degenerate vacuum gravitational fields
33 Killing vectors and groups of motion
33.3 Killing vectors of some simple spaces
33.4 Relations between the curvature tensor and Killing vectors
33.6 Killing vectors and conservation laws
34 A survey of some selected classes of exact solutions
34.1 Degenerate vacuum solutions
34.2 Vacuum solutions with special symmetry properties
34.3 Perfect fluid solutions with special symmetry properties
VI. Gravitational collapse and black holes
35 The Schwarzschild singularity
35.1 How does one examine the singular points of a metric?
35.2 Radial geodesics near r = 2M
35.3 The Schwarzschild solution in other coordinate systems
35.4 The Schwarzschild solution as a black hole
36 Gravitational collapse – the possible life history of a spherically symmetric star
36.1 The evolutionary phases of a spherically symmetric star
36.2 The critical mass of a star
36.3 Gravitational collapse of spherically symmetric dust
Further reading for Chapter 36
37.2 Gravitational collapse – the possible life history of a rotating star
37.3 Some properties of black holes
37.4 Are there black holes?
Further reading for Chapter 37
38 Black holes are not black – Relativity Theory and Quantum Theory Theory and Quantum Theory
38.2 Unifled quantum field theory and quantization of the gravitational field
38.3 Semiclassical gravity
38.4 Quantization in a given classical gravitational field
38.5 Black holes are not black – the thermodynamics of black holes
Further reading for Chapter 38
39 The conformal structure of infinity
39.1 The problem and methods to answer it
39.2 Infinity of the three-dimensional Euclidean space (E3)
39.3 The conformal structure of Minkowski space
39.4 Asymptotically flat gravitational fields
39.5 Examples of Penrose diagrams
40 Robertson–Walker metrics and their properties
40.1 The cosmological principle and Robertson–Walker metrics
40.2 The motion of particles and photons
40.3 Distance definitions and horizons
40.4 Some remarks on physics in closed universes
41 The dynamics of Robertson–Walker metrics and the Friedmann universes
41.1 The Einstein field equations for Robertson–Walker metrics
41.2 The most important Friedmann universes
41.3 Consequences of the field equations for models with arbitrary equation of state having positive pressure and positive rest mass density
42 Our universe as a Friedmann model
42.1 Redshift and mass density
42.2 The earliest epochs of our universe and the cosmic background radiation
42.3 A Schwarzschild cavity in the Friedmann universe
43 General cosmological models
43.1 What is a cosmological model?
43.2 Solutions of Bianchi type I with dust
43.4 Singularity theorems
Further reading for Chapter 43
Alternative textbooks on relativity and useful review volumes
Monographs and research articles
Relativity
：An Introduction to Special and General Relativity
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