| Description |
1 online resource (566 p.) |
| Series |
Graduate Texts in Physics |
|
Graduate texts in physics.
|
| Contents |
Intro -- Foreword -- Preface to the English Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Outline of Volume II -- Outline of Volume III -- 1 Topological Spaces in Brief -- 1.1 The ABCs of Set Theory -- 1.2 Topological Spaces -- 1.3 Compactness [Optional Reading] -- Exercises -- Reference -- 2 Manifolds and Tensor Fields -- 2.1 Differentiable Manifolds -- 2.2 Tangent Vectors and Tangent Vector Fields -- 2.2.1 Tangent Vectors -- 2.2.2 Tangent Vector Fields on Manifolds -- 2.3 Dual Vector Fields -- 2.4 Tensor Fields -- 2.5 Metric Tensor Fields |
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2.6 The Abstract Index Notation -- Exercises -- References -- 3 The Riemann (Intrinsic) Curvature Tensor -- 3.1 Derivative Operators -- 3.2 Derivative and Parallel Transport of a Vector Field Along a Curve -- 3.2.1 Parallel Transport of a Vector Field Along a Curve -- 3.2.2 The Derivative Operator Associated with a Metric -- 3.2.3 Relationship Between the Derivative and Parallel Transport of a Vector Field Along a Curve -- 3.3 Geodesics -- 3.4 The Riemann Curvature Tensor -- 3.4.1 Definition and Properties of the Riemann Curvature -- 3.4.2 Computing Riemann Curvature from a Metric |
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3.5 The Intrinsic Curvature and the Extrinsic Curvature -- Exercises -- References -- 4 Lie Derivatives, Killing Fields and Hypersurfaces -- 4.1 Maps of Manifolds -- 4.2 Lie Derivatives -- 4.3 Killing Vector Fields -- 4.4 Hypersurfaces -- Exercises -- References -- 5 Differential Forms and Their Integrals -- 5.1 Differential Forms -- 5.2 Integration on Manifolds -- 5.3 Stokes's Theorem -- 5.4 Volume Elements -- 5.5 Integrating Functions on Manifolds, Gauss's Theorem -- 5.6 Dual Differential Forms -- 5.7 Computing the Riemann Curvature Using the Tetrad Method [Optional Reading] -- Exercises |
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6.4 The Energy-Momentum Tensor of Continuous Media -- 6.5 Perfect Fluid Dynamics -- 6.6 Electrodynamics -- 6.6.1 Electromagnetic Fields and 4-Current Densities -- 6.6.2 Maxwell's Equations -- 6.6.3 Lorentz 4-Force -- 6.6.4 The Energy-Momentum Tensor of an Electromagnetic Field -- 6.6.5 Electromagnetic 4-Potential and Its Equation of Motion, Electromagnetic Waves -- 6.6.6 The Doppler Effect on a Light Wave -- Exercises -- References -- 7 Foundations of General Relativity -- 7.1 Gravity and Spacetime Geometry -- 7.2 Physical Laws in Curved Spacetime |
| Summary |
This book, the first in a three-volume set, explains general relativity using the mathematical tool of differential geometry. The book consists of ten chapters, the first five of which introduce differential geometry, which is widely applicable even outside the field of relativity. Chapter 6 analyzes special relativity using geometric language. In turn, the last four chapters introduce readers to the fundamentals of general relativity. Intended for beginners, this volume includes numerous exercises and worked-out example in each chapter to facilitate the learning experience. Chiefly written for graduate-level courses, the books content will also benefit upper-level undergraduate students, and can be used as a reference guide for practicing theoretical physicists |
| Bibliography |
References -- 6 Special Relativity -- 6.1 Foundations of the 4-Dimensional Formulation -- 6.1.1 Preliminaries -- 6.1.2 The Background Spacetime of Special Relativity -- 6.1.3 Inertial Observers and Inertial Frames -- 6.1.4 Proper Time and Coordinate Time -- 6.1.5 Spacetime Diagrams -- 6.1.6 Spacetime Structure: Special Relativity Versus Pre-Relativity Physics -- 6.2 Interesting Typical Effects -- 6.2.1 Length Contraction -- 6.2.2 Time Dilation -- 6.2.3 The Twin ̀̀Paradox'' -- 6.2.4 The Garage ̀̀Paradox'' -- 6.3 Kinematics and Dynamics of a Point Mass |
| Notes |
7.3 Fermi-Walker Transport and Non-Rotating Observers |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed September 12, 2023) |
| Subject |
Geometry, Differential.
|
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General relativity (Physics)
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| Form |
Electronic book
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| Author |
Zhou, Bin, author
|
|
Jia, Weizhen, translator
|
| ISBN |
9789819900220 |
|
9819900220 |
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