Efnisyfirlit

• 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

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