Relativity : special, general, and cosmological

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Relativity : special, general, and cosmological / Wolfgang Rindler

版:: 2nd ed
資料種別:: 図書
出版情報:: Oxford : Oxford University Press, 2006
形態:: xv, 430 p. ; 24 cm
著者名:: Rindler, Wolfgang, 1924- <DA00245121>
ISBN:: 9780198567318 [0198567316] (: hbk)
9780198567325 [0198567324] (: pbk)
書誌ID:: BA76906348

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注記:

Includes index

主題:

Cosmology; Relativity (Physics)

言語:

英語

目次情報:

Introduction

From Absolute Space and Time to Influenceable Spacetime: An Overview / 1：

Special Relativity / I：

Foundations of Special Relativity: The Lorentz Transformation / 2：

Relativistic Kinematics / 3：

Relativistic Optics / 4：

Spacetime and Four-vectors / 5：

Relativistic Particle Mechanics / 6：

Four-tensors: Electromagnetism in Vacuum / 7：

General Relativity / II：

Curved Spaces and the Basic Ideas of General Relativity / 8：

Static and Stationary Spacetimes / 9：

Geodesics, Curvature Tensor, and Vacuum Field Equations / 10：

The Schwarzschild Metric / 11：

Black Holes and Kruskal Space / 12：

An Exact Plane Gravitational Wave / 13：

The Full Field Equations: De Sitter Space / 14：

Linearized General Relativity / 15：

Cosmology / III：

Cosmological Spacetimes / 16：

Light Propagation in FRW Universes / 17：

Dynamics of FRW Universes / 18：

Appendix: Curvture Tensor Components for the Diagonal Metric

Index

From absolute space and time to influenceable spacetime: an overview

Definition of relativity / 1.1：

Newton's laws and inertial frames / 1.2：

The Galilean transformation / 1.3：

Newtonian relativity / 1.4：

Objections to absolute space; Mach's principle / 1.5：

The ether / 1.6：

Michelson and Morley's search for the ether / 1.7：

Lorentz's ether theory / 1.8：

Origins of special relativity / 1.9：

Further arguments for Einstein's two postulates / 1.10：

Cosmology and first doubts about inertial frames / 1.11：

Inertial and gravitational mass / 1.12：

Einstein's equivalence principle / 1.13：

Preview of general relativity / 1.14：

Caveats on the equivalence principle / 1.15：

Gravitational frequency shift and light bending / 1.16：

Exercises 1

Foundations of special relativity; The Lorentz transformation

On the nature of physical theories / 2.1：

Basic features of special relativity / 2.2：

Relativistic problem solving / 2.3：

Relativity of simultaneity, time dilation and length contraction: a preview / 2.4：

The relativity principle and the homogeneity and isotropy of inertial frames / 2.5：

The coordinate lattice; Definitions of simultaneity / 2.6：

Derivation of the Lorentz transformation / 2.7：

Properties of the Lorentz transformation / 2.8：

Graphical representation of the Lorentz transformation / 2.9：

The relativistic speed limit / 2.10：

Which transformations are allowed by the relativity principle? / 2.11：

Exercises 2

Relativistic kinematics

World-picture and world-map / 3.1：

Length contraction / 3.3：

Length contraction paradox / 3.4：

Time dilation; The twin paradox / 3.5：

Velocity transformation; Relative and mutual velocity / 3.6：

Acceleration transformation; Hyperbolic motion / 3.7：

Rigid motion and the uniformly accelerated rod / 3.8：

Exercises 3

Relativistic optics

The drag effect / 4.1：

The Doppler effect / 4.3：

Aberration / 4.4：

The visual appearance of moving objects / 4.5：

Exercises 4

Spacetime and four-vectors

The discovery of Minkowski space / 5.1：

Three-dimensional Minkowski diagrams / 5.2：

Light cones and intervals / 5.3：

Three-vectors / 5.4：

Four-vectors / 5.5：

The geometry of four-vectors / 5.6：

Plane waves / 5.7：

Exercises 5

Relativistic particle mechanics

Domain of sufficient validity of Newtonian mechanics / 6.1：

The axioms of the new mechanics / 6.2：

The equivalence of mass and energy / 6.3：

Four-momentum identities / 6.4：

Relativistic billiards / 6.5：

The zero-momentum frame / 6.6：

Threshold energies / 6.7：

Light quanta and de Broglie waves / 6.8：

The Compton effect / 6.9：

Four-force and three-force / 6.10：

Exercises 6

Four-tensors; Electromagnetism in vacuum

Tensors: Preliminary ideas and notations / 7.1：

Tensors: Definition and properties / 7.2：

Maxwell's equations in tensor form / 7.3：

The four-potential / 7.4：

Transformation of e and b; The dual field / 7.5：

The field of a uniformly moving point charge / 7.6：

The field of an infinite straight current / 7.7：

The energy tensor of the electromagnetic field / 7.8：

From the mechanics of the field to the mechanics of material continua / 7.9：

Exercises 7

Curved spaces and the basic ideas of general relativity

Curved surfaces / 8.1：

Curved spaces of higher dimensions / 8.2：

Riemannian spaces / 8.3：

A plan for general relativity / 8.4：

Exercises 8

Static and stationary spacetimes

The coordinate lattice / 9.1：

Synchronization of clocks / 9.2：

First standard form of the metric / 9.3：

Newtonian support for the geodesic law of motion / 9.4：

Symmetries and the geometric characterization of static and stationary spacetimes / 9.5：

Canonical metric and relativistic potentials / 9.6：

The uniformly rotating lattice in Minkowski space / 9.7：

Exercises 9

Geodesics, curvature tensor and vacuum field equations

Tensors for general relativity / 10.1：

Geodesics / 10.2：

Geodesic coordinates / 10.3：

Covariant and absolute differentiation / 10.4：

The Riemann curvature tensor / 10.5：

Einstein's vacuum field equations / 10.6：

Exercises 10

The Schwarzschild metric

Derivation of the metric / 11.1：

Properties of the metric / 11.2：

The geometry of the Schwarzschild lattice / 11.3：

Contributions of the spatial curvature to post-Newtonian effects / 11.4：

Coordinates and measurements / 11.5：

The gravitational frequency shift / 11.6：

Isotropic metric and Shapiro time delay / 11.7：

Particle orbits in Schwarzschild space / 11.8：

The precession of Mercury's orbit / 11.9：

Photon orbits / 11.10：

Deflection of light by a spherical mass / 11.11：

Gravitational lenses / 11.12：

de Sitter precession via rotating coordinates / 11.13：

Exercises 11

Black holes and Kruskal space

Schwarzschild black holes / 12.1：

Potential energy; A general-relativistic 'proof' of E = mc[superscript 2] / 12.2：

The extendibility of Schwarzschild spacetime / 12.3：

The uniformly accelerated lattice / 12.4：

Kruskal space / 12.5：

Black-hole thermodynamics and related topics / 12.6：

Exercises 12

An exact plane gravitational wave

The plane-wave metric / 13.1：

When wave meets dust / 13.3：

Inertial coordinates behind the wave / 13.4：

When wave meets light / 13.5：

The Penrose topology / 13.6：

Solving the field equation / 13.7：

Exercises 13

The full field equations; de Sitter space

The laws of physics in curved spacetime / 14.1：

At last, the full field equations / 14.2：

The cosmological constant / 14.3：

Modified Schwarzschild space / 14.4：

de Sitter space / 14.5：

Anti-de Sitter space / 14.6：

Exercises 14

Linearized general relativity

The basic equations / 15.1：

Gravitational waves; The TT gauge / 15.2：

Some physics of plane waves / 15.3：

Generation and detection of gravitational waves / 15.4：

The electromagnetic analogy in linearized GR / 15.5：

Exercises 15

Cosmological spacetimes

The basic facts / 16.1：

Beginning to construct the model / 16.2：

Milne's model / 16.3：

The Friedman-Robertson-Walker metric / 16.4：

Robertson and Walker's theorem / 16.5：

Exercises 16

Light propagation in FRW universes

Representation of FRW universes by subuniverses / 17.1：

The cosmological frequency shift / 17.2：

Cosmological horizons / 17.3：

The apparent horizon / 17.4：

Observables / 17.5：

Exercises 17

Dynamics of FRW universes

Applying the field equations / 18.1：

What the field equations tell us / 18.2：

The Friedman models / 18.3：

Once again, comparison with observation / 18.4：

Inflation / 18.5：

The anthropic principle / 18.6：

Exercises 18

Curvature tensor components for the diagonal metric / Appendix：

Introduction

From Absolute Space and Time to Influenceable Spacetime: An Overview / 1：

Special Relativity / I：

Foundations of Special Relativity: The Lorentz Transformation / 2：

Relativistic Kinematics / 3：

Relativistic Optics / 4：

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