General relativity : a geometric approach

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General relativity : a geometric approach / Malcolm Ludvigsen

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 1999
形態:: xii, 217 p. ; 27 cm
著者名:: Ludvigsen, Malcolm, 1946-
ISBN:: 9780521630191 [0521630193] (: hbk)
9780521639767 [052163976X] (: pbk)
書誌ID:: BA42643270

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注記:

Includes bibliographical references (p. 213-214) and index

主題:

General relativity (Physics); Geometrodynamics; Space and time

言語:

英語

目次情報:

Preface

The Concept of Spacetime / Part 1：

Introduction / 1：

Exercises

Events and Spacetime / 2：

Events / 2.1：

Inertial Particles / 2.2：

Light and Null Cones / 2.3：

Flat Spacetime and Special Relativity / Part 2：

Flat Spacetime / 3：

Distance, Time, and Angle / 3.1：

Speed and the Doppler Effect / 3.2：

The Geometry of Flat Spacetime / 4：

Spacetime Vectors / 4.1：

The Spacetime Metric / 4.2：

Volume and Particle Density / 4.3：

Energy / 5：

Energy and Four-Momentum / 5.1：

The Energy-Momentum Tensor / 5.2：

General States of Matter / 5.3：

Perfect Fluids / 5.4：

Acceleration and the Maxwell Tensor / 5.5：

Tensors / 6：

Tensors at a Point / 6.1：

The Abstract Index Notation / 6.2：

Tensor Fields / 7：

Congruences and Derivations / 7.1：

Lie Derivatives / 7.2：

Field Equations / 8：

Conservation Laws

Maxwell's Equations / 8.2：

Charge, Mass, and Angular Momentum / 8.3：

Curved Spacetime and Gravity / Part 3：

Curved Spacetime / 9：

Spacetime as a Manifold / 9.1：

The Covariant Derivative / 9.2：

The Curvature Tensor / 9.4：

Constant Curvature / 9.5：

Curvature and Gravity / 10：

Geodesics / 10.1：

Einstein's Field Equation / 10.2：

Gravity as an Attractive Force / 10.3：

Null Congruences / 11：

Surface-Forming Null Congruences / 11.1：

Twisting Null Congruences / 11.2：

Asymptotic Flatness and Symmetries / 12：

Asymptotically Flat Spacetimes / 12.1：

Killing Fields and Stationary Spacetimes / 12.2：

Kerr Spacetime / 12.3：

Energy and Intrinsic Angular Momentum / 12.4：

Schwarzschiid Geometries and Spacetimes / 13：

Schwarzschild Geometries / 13.1：

Geodesics in a Schwarzschild Spacetime / 13.2：

Three Classical Tests of General Relativity / 13.3：

Schwarzschild Spacetimes / 13.4：

Black Holes and Singularities / 14：

Spherical Gravitational Collapse / 14.1：

Singularities / 14.2：

Black Holes and Horizons / 14.3：

Stationary Black Holes and Kerr Spacetime / 14.4：

The Ergosphere and Energy Extraction / 14.5：

Black-Hole Thermodynamics / 14.6：

Cosmology / Part 4：

The Spacetime of the Universe / 15：

The Cosmological Principle / 15.1：

Cosmological Red Shifts / 15.2：

The Evolution of the Universe / 15.3：

Horizons / 15.4：

Relativistic Cosmology / 16：

Friedmann Universes / 16.1：

The Cosmological Constant / 16.2：

The Hot Big-Bang Model / 16.3：

Blackbody Radiation / 16.4：

The Origin of the Background Radiation / 16.5：

A Model Universe / 16.6：

Solutions and Hints to Selected Exercises

Bibliography

Index

Preface

The Concept of Spacetime / Part 1：

Introduction / 1：

Exercises

Events and Spacetime / 2：

Events / 2.1：

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