Relativity Made Relatively Easy

Name: Relativity Made Relatively Easy | Volume 1
Brand: OUP eBook
Price: 63.69 EUR
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Volume 1

Andrew M. Steane(Autor*in)

OUP eBook (Verlag)

1. Auflage

Erschienen am 5. Oktober 2012

436 Seiten

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978-0-19-165041-3 (ISBN)

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Inhalt

Cover
Contents
I: The relativistic world
1 Basic ideas
1.1 Newtonian physics
1.2 Special Relativity
1.3 Matrix methods
1.4 Spacetime diagrams
Exercises
2 The Lorentz transformation
2.1 Introducing the Lorentz transformation
2.2 Velocities
2.3 Lorentz invariance and 4-vectors
2.4 Lorentz-invariant quantities
2.5 Basic 4-vectors
2.6 The joy of invariants
2.7 Summary
Exercises
3 Moving light sources
3.1 The Doppler effect
3.2 Aberration and the headlight effect
3.3 Visual appearances*
Exercises
4 Dynamics
4.1 Force
4.2 Motion under a pure force
Exercises
5 The conservation of energy-momentum
5.1 Elastic collision, following Lewis and Tolman
5.2 Energy-momentum conservation using 4-vectors
5.3 Collisions
5.4 Elastic collisions
5.5 Composite systems
5.6 Energy flux, momentum density, and force
Exercises
6 Further kinematics
6.1 The Principle of Most Proper Time
6.2 Four-dimensional gradient
6.3 Current density, continuity
6.4 Wave motion
6.5 Acceleration and rigidity
6.6 General Lorentz boost
6.7 Lorentz boosts and rotations
6.8 Generators of boosts and rotations
6.9 The Lorentz group*
Exercises
7 Relativity and electromagnetism
7.1 Definition of electric and magnetic fields
7.2 Maxwell's equations
7.3 The fields due to a moving point charge
7.4 Covariance of Maxwell's equations
7.5 Introducing the Faraday tensor
Exercises
8 Electromagnetic radiation
8.1 Plane waves in vacuum
8.2 Solution of Maxwell's equations for a given charge distribution
8.3 Radiated power
Exercises
II: An introduction to General Relativity
9 The Principle of Equivalence
9.1 Free fall
9.2 The uniformly accelerating reference frame
9.3 Newtonian gravity from the Principle of Most Proper Time
9.4 Gravitational redshift and energy conservation
Exercises
10 Warped spacetime
10.1 Two-dimensional spatial surfaces
10.2 Three spatial dimensions
10.3 Time and space together
10.4 Gravity and curved spacetime
Exercises
11 Physics from the metric
11.1 Example exact solutions
11.2 Schwarzschild metric: basic properties
11.3 Geometry of Schwarzschild solution
11.4 Gravitational lensing
11.5 Black holes
11.6 What next?
Exercises
III: Further Special Relativity
12 Tensors and index notation
12.1 Index notation in a nutshell
12.2 Tensor analysis
12.3 Antisymmetric tensors and the dual
Exercises
13 Rediscovering electromagnetism
13.1 Fundamental equations
13.2 Invariants of the electromagnetic field
Exercises
14 Lagrangian mechanics
14.1 Classical Lagrangian mechanics
14.2 Relativistic motion
14.3 Conservation
14.4 Equation of motion in General Relativity*
Exercises
15 Angular momentum*
15.1 Conservation of angular momentum
15.2 Spin
Exercises
16 Energy density
16.1 Introducing the stress-energy tensor
16.2 Stress-energy tensor for an arbitrary system
16.3 Conservation of energy and momentum for a fluid
16.4 Electromagnetic energy and momentum
16.5 Field and matter pushing on one another
Exercises
17 What is spacetime?
Appendix A: Some basic arguments
A.1 Early experiments
A.2 Simultaneity and radar coordinates
A.3 Proper time and time dilation
A.4 Lorentz contraction
A.5 Doppler effect, addition of velocities
Appendix B: Constants and length scales
Appendix C: Derivatives and index notation
Appendix D: The field of an arbitrarily moving charge
D.1 Light-cone volume element
D.2 The field tensor
Bibliography
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Z

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