A First Course in General Relativity

✍ Scribed by Bernard Schutz

• Publisher: Cambridge University Press
• Year: 2022
• Tongue: English
• Leaves: 516
• Edition: 3
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover
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