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001476500 001__ 1476500
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001476500 019__ $$a1395537462$$a1396895962
001476500 020__ $$a9789819900220$$q(electronic bk.)
001476500 020__ $$a9819900220$$q(electronic bk.)
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001476500 0247_ $$a10.1007/978-981-99-0022-0$$2doi
001476500 035__ $$aSP(OCoLC)1396063358
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001476500 049__ $$aISEA
001476500 050_4 $$aQA641
001476500 08204 $$a530.11$$223/eng/20230912
001476500 1001_ $$aLiang, Canbin,$$eauthor.
001476500 24010 $$aWei fen ji he yu guang yi xiang dui lun.$$lEnglish
001476500 24510 $$aDifferential geometry and general relativity.$$nVolume 1 /$$cCambin Liang, Bin Zhou.
001476500 260__ $$aSingapore :$$bSpringer,$$c2023.
001476500 300__ $$a1 online resource (566 p.).
001476500 336__ $$atext$$btxt$$2rdacontent
001476500 337__ $$acomputer$$bc$$2rdamedia
001476500 338__ $$aonline resource$$bcr$$2rdacarrier
001476500 4901_ $$aGraduate Texts in Physics
001476500 500__ $$a7.3 Fermi-Walker Transport and Non-Rotating Observers
001476500 504__ $$aReferences -- 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
001476500 504__ $$aIncludes bibliographical references and index.
001476500 5050_ $$aIntro -- 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
001476500 5058_ $$a2.6 The Abstract Index Notation -- Exercises -- References -- 3 The Riemann (Intrinsic) Curvature Tensor -- 3.1 Derivative Operators -- 3.2 Derivative and Parallel Transport of a Vector Field Along a Curve -- 3.2.1 Parallel Transport of a Vector Field Along a Curve -- 3.2.2 The Derivative Operator Associated with a Metric -- 3.2.3 Relationship Between the Derivative and Parallel Transport of a Vector Field Along a Curve -- 3.3 Geodesics -- 3.4 The Riemann Curvature Tensor -- 3.4.1 Definition and Properties of the Riemann Curvature -- 3.4.2 Computing Riemann Curvature from a Metric
001476500 5058_ $$a3.5 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
001476500 5058_ $$a6.4 The Energy-Momentum Tensor of Continuous Media -- 6.5 Perfect Fluid Dynamics -- 6.6 Electrodynamics -- 6.6.1 Electromagnetic Fields and 4-Current Densities -- 6.6.2 Maxwell's Equations -- 6.6.3 Lorentz 4-Force -- 6.6.4 The Energy-Momentum Tensor of an Electromagnetic Field -- 6.6.5 Electromagnetic 4-Potential and Its Equation of Motion, Electromagnetic Waves -- 6.6.6 The Doppler Effect on a Light Wave -- Exercises -- References -- 7 Foundations of General Relativity -- 7.1 Gravity and Spacetime Geometry -- 7.2 Physical Laws in Curved Spacetime
001476500 506__ $$aAccess limited to authorized users.
001476500 520__ $$aThis book, the first in a three-volume set, explains general relativity using the mathematical tool of differential geometry. The book consists of ten chapters, the first five of which introduce differential geometry, which is widely applicable even outside the field of relativity. Chapter 6 analyzes special relativity using geometric language. In turn, the last four chapters introduce readers to the fundamentals of general relativity. Intended for beginners, this volume includes numerous exercises and worked-out example in each chapter to facilitate the learning experience. Chiefly written for graduate-level courses, the books content will also benefit upper-level undergraduate students, and can be used as a reference guide for practicing theoretical physicists.
001476500 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed September 12, 2023).
001476500 650_0 $$aGeometry, Differential.
001476500 650_0 $$aGeneral relativity (Physics)
001476500 650_6 $$aGéométrie différentielle.
001476500 650_6 $$aRelativité générale (Physique)
001476500 655_0 $$aElectronic books.
001476500 7001_ $$aZhou, Bin,$$eauthor.
001476500 7001_ $$aJia, Weizhen,$$etranslator.
001476500 77608 $$iPrint version:$$aLiang, Canbin$$tDifferential Geometry and General Relativity$$dSingapore : Springer,c2023$$z9789819900213
001476500 830_0 $$aGraduate texts in physics.
001476500 852__ $$bebk
001476500 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-99-0022-0$$zOnline Access$$91397441.1
001476500 909CO $$ooai:library.usi.edu:1476500$$pGLOBAL_SET
001476500 980__ $$aBIB
001476500 980__ $$aEBOOK
001476500 982__ $$aEbook
001476500 983__ $$aOnline
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