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• Half-title
• Title page
• Copyright information
• Contents
• Preface to the third edition
• Preface to the second edition
• Preface to the first edition
• 1 Special relativity
• 1.1 Fundamental principles of special relativity theory (SR)
• 1.2 Definition of an inertial observer in SR
• 1.3 New units
• 1.4 Spacetime diagrams
• 1.5 Construction of the coordinates used by another observer
• 1.6 Invariance of the interval
• 1.7 Invariant hyperbolae
• 1.8 Particularly important results
• 1.9 The Lorentz transformation
• 1.10 The velocity-addition law
• 1.11 Paradoxes and physical intuition
• 1.12 Bibliography
• 1.13 Appendix: The twin ‘paradox’ dissected
• Exercises
• 2 Vector analysis in special relativity
• 2.1 Definition of a vector
• 2.2 Vector algebra
• 2.3 The four-velocity
• 2.4 The four-momentum and its conservation
• 2.5 Scalar product
• 2.6 Applications
• 2.7 Photons
• 2.8 Bibliography
• Exercises
• 3 Tensor analysis in special relativity
• 3.1 The metric tensor
• 3.2 Definition of tensors
• 3.3 The [choose(0)(1)] tensors: one-forms
• 3.4 Gradient of a function is a one-form
• 3.5 The [choose(0)(2)] tensors
• 3.6 Metric as a mapping of vectors into one-forms
• 3.7 Finally: [choose(M)(N)] tensors
• 3.8 Index ‘raising’ and ‘lowering’
• 3.9 Differentiation of tensors
• 3.10 Bibliography
• Exercises
• 4 Perfect fluids in special relativity
• 4.1 Fluids
• 4.2 Dust: the number-flux vector [vec(N)]
• 4.3 One-forms and surfaces
• 4.4 Dust again: the stress–energy tensor
• 4.5 General fluids
• 4.6 Conservation of energy–momentum
• 4.7 Perfect fluids
• 4.8 Importance for general relativity
• 4.9 Gauss’ law
• 4.10 Bibliography
• Exercises
• 5 Preface to curvature
• 5.1 On the relation of gravitation to curvature
• 5.2 Tensor algebra in polar coordinates
• 5.3 Tensor calculus in polar coordinates
• 5.4 Christoffel symbols and the metric
• 5.5 Noncoordinate bases
• 5.6 Looking ahead
• 5.7 Bibliography
• Exercises
• 6 Curved manifolds
• 6.1 Differentiable manifolds and tensors
• 6.2 Riemannian manifolds
• 6.3 Covariant differentiation on a general manifold
• 6.4 Parallel transport, geodesics, and curvature
• 6.5 The curvature tensor
• 6.6 Bianchi identities; Ricci and Einstein tensors
• 6.7 Curvature in perspective
• 6.8 Bibliography
• Exercises
• 7 Physics in a curved spacetime
• 7.1 The transition from differential geometry to gravity
• 7.2 Physics in slightly curved spacetimes
• 7.3 Curved intuition
• 7.4 Conserved quantities
• 7.5 Bibliography
• Exercises
• 8 The Einstein field equations
• 8.1 Purpose and justification of the field equations
• 8.2 Einstein’s equations
• 8.3 Einstein’s equations for weak gravitational fields
• 8.4 Newtonian gravitational fields
• 8.5 Bibliography
• Exercises
• 9 Fundamentals of gravitational radiation
• 9.1 The role of general relativity in the physical Universe
• 9.2 The propagation of gravitational waves
• 9.3 The detection of gravitational waves
• 9.4 The generation of gravitational waves
• 9.5 The energy carried away by gravitational waves
• 9.6 Standard sirens
• 9.7 Bibliography
• Exercises
• 10 Spherical solutions for stars
• 10.1 Coordinates for spherically symmetric spacetimes
• 10.2 Static spherically symmetric spacetimes
• 10.3 Static perfect-fluid Einstein equations
• 10.4 The exterior geometry
• 10.5 The interior structure of the star
• 10.6 Exact interior solutions
• 10.7 Realistic stars and gravitational collapse
• 10.8 Bibliography
• Exercises
• 11 Schwarzschild geometry and black holes
• 11.1 Trajectories in the Schwarzschild spacetime
• 11.2 Nature of the surface r = 2M
• 11.3 General black holes
• 11.4 Real black holes in astronomy
• 11.5 Hawking radiation
• 11.6 Bibliography
• Exercises
• 12 Gravitational wave astronomy
• 12.1 Overview
• 12.2 Astrophysical sources of gravitational waves
• 12.3 Finding weak signals in noise: what is a detection?
• 12.4 The first LIGO and Virgo detections
• 12.5 Bibliography
• Exercises
• 13 Cosmology
• 13.1 What is cosmology?
• 13.2 Cosmological kinematics: observing our expanding Universe
• 13.3 Cosmological dynamics: understanding the expanding Universe
• 13.4 Physical cosmology: the evolution of the Universe we observe
• 13.5 Bibliography
• Exercises
• Appendix A Summary of linear algebra
• References
• Index