A First Course in General Relativity

Höfundur: Bernard Schutz (Útgáfa: 3)
A First Course in General Relativity

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Clarity, readability, and rigor combine in the third edition of this widely used textbook to provide the first step into general relativity for advanced undergraduates with a minimal background in mathematics. Topics within relativity that fascinate astrophysics researchers and students alike are covered with Schutz's characteristic ease and authority, from black holes to relativistic objects, from pulsars to the study of the Universe as a whole.

This third edition contains discoveries by astronomers that require general relativity for their explanation; two chapters on gravitational waves, including direct detections of gravitational waves and their observations' impact on cosmological measurements; new information on black holes and neutron stars; and greater insight into the expansion of the Universe. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, while the informal writing style and worked examples make the subject matter easily accessible.

Nánar um bókina

Útgefandi
Cambridge University Press
ISBN
9781108586597
Print ISBN
9781108492676
Format
Page Fidelity (PDF)
Útgáfa
3
Höfundar
Bernard Schutz
Tungumál
English
Útgefið
2022-06-30
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • 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