Preface
Author biography
1 Why relativity?
1.1 The Galilei invariance of Newtonian mechanics
1.2 The need for special relativity
1.3 The need for general relativity
2 A first look at notions from geometry
2.1 Vectors and tensors
2.2 Curvilinear coordinates
3 The tangents of spacetime: special relativity
3.1 Lorentz transformations and the relativity of space and time
3.2 Consequences of Lorentz symmetry
3.3 The general Lorentz transformation
4 Relativistic dynamics
4.1 Energy-momentum vectors and the relativistic Newton equation
4.2 The manifestly covariant formulation of electrodynamics
4.3 Action principles for relativistic particles
4.4 Current densities and stress-energy tensors
5 Differential geometry: the kinematics of curved spacetime
5.1 More geometry: surfaces in R3
5.2 Covariant derivatives and Christoffel symbols
5.3 Transformations of tensors and Christoffel symbols
6 Particles in curved spacetime
6.1 Motion of a particle in spacetime
6.2 Slow particles in a weak gravitational field
6.3 Local inertial frames
6.4 Symmetric spaces and conservation laws
7 The dynamics of spacetime: the Einstein equation
7.1 Geodesic deviation and curvature
7.2 The Einstein equation
7.3 The Schwarzschild metric: The gravitational field outside a
non-rotating star
7 4 The interior of Schwarzschild black holes
7.5 Maximal extension of the Schwarzschild spacetime and wormholes
8 Massive particles in the Schwarzschild spacetime
8.1 Massive particles in t-independent radially sym metric spacetimes
8.2 Radial motion in terms of the effective potential
8.3 The shape of the trajectory
8.4 Clocks in the Schwarzschild spacetime
8.5 Escape velocities and infall times
9 Massless particles in the Schwarzschild spacetime
9.1 Equations of motion
9.2 Deflection of light in a gravitational field
9.3 Apparent photon speeds and radial infall
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