List of exercises List of projects Preface How to use this book 1 Special relativity 1.1 Introduction 1.2 The principles of special relativity 1.3 Transformation of coordinates and velocities 1.3.1 Lorentz transformation 1.3.2 Transformation of velocities 1.3.3 Lorentz boost in an arbitrary direction 1.4 Four-vectors 1.4.1 Four-velocity and acceleration 1.5 Tensors 1.6 Tensors as geometrical objects 1.7 Volume and surface integrals in four dimensions 1.8 Particle dynamics 1.9 The distribution function and its moments 1.10 The Lorentz group and Pauli matrices 2 Scalar and electromagnetic fields in special relativity 2.1 Introduction 2.2 External fields of force 2.3 Classical scalar field 2.3.1 Dynamics of a particle interacting with a scalar field 2.3.2 Action and dynamics of the scalar field 2.3.3 Energy-momentum tensor for the scalar field 2.3.4 Free field and the wave solutions 2.3.5 Why does the scalar field lead to an attractive force? 2.4 Electro magnetic field 2.4.1 Charged particle in an electromagnetic field 2.4.2 Lorentz transformation of electric and magnetic fields 2.4.3 Current vector 2.5 Motion in the Coulomb field 2.6 Motion in a constant electric field 2.7 Action principle for the vector field 2.8 Maxwell's equations 2.9 Energy and momentum of the electromagnetic field 2.10 Radiation from an accelerated charge 2.11 Larmor formula and radiation reaction 3 Gravity and spacetime geometry: the inescapable connection 3.1 Introduction 3.2 Field theoretic approaches to gravity 3.3 Gravity as a scalar field 3.4 Second rank tensor theory of gravity 3.5 The principle of equivalence and the geometrical description of ravity 3.5.1 Uniformly accelerated observer 3.5.2 Gravity and the fiow of time 4 Metric tensor, geodesics and covariant derivative 4.1 Introduction 4.2 Metric tensor and gravity 4.3 Tensor algebra in curved spacetime 4.4 Volume and surface integrals 4.5 Geodesic curves 4.5.1 Properties of geodesic curves 4.5.2 Affine parameter and null geodesics 4.6 Covariant derivative 4.6.1 Geometrical interpretation of the covariant derivative 4.6.2 Manipulation of covariant derivatives 4.7 Parallel transport 4.8 Lie transport and Killing vectors 4.9 Fermi-Walker transport 5 Curvature of spacetime 5.1 Introduction 5.2 Three perspectives on the spacetime curvature 5.2.1 Parallel transport around a closed curve 5.2.2 Non-commutativity of covariant derivatives …… 6 Einstein's field equations and gravitational dynamics 7 Spherically symmetric geometry 8 Black holes 9 Gravitational waves 10 RelatMstic cosmology 11 Differential forms and exterior calculus 12 Hamiltonian structure of general relativity 13 Evolution of cosmological perturbations 14 Quantum field theory in curved spacetime 15 Gravity in higher and lower dimensions 16 Gravity as an emergent phenomenon
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