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About this book :-
Tensors Mathematics of Differential Geometry and Relativity written by
Zafar Ahsan.
Book Detail :-
Title: Tensors Mathematics of Differential Geometry and Relativity
Edition:
Author(s): Zafar Ahsan
Publisher:
Series:
Year:
Pages: 11
Type: PDF
Language: Englsih
ISBN:
Country:
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Book Contents :-
Tensors Mathematics of Differential Geometry and Relativity written by
Zafar Ahsan
cover the following topics.
'
Tensors and Their Algebra
Introduction, Transformation of Coordinates, Summation Convention, Kronecker Delta, Scalar, Contravariant and Covariant Vectors, Tensors of Higher Rank, Symmetry of Tensors, Algebra of Tensors, Irreducible Tensor, Exercises
Riemannian Space and Metric Tensor
Introduction, The Metric Tensor, Raising and Lowering of Indices—Associated Tensor, Vector Magnitude, Relative and Absolute Tensors, Levi-Civita Tensor, Exercises
Christoffel Symbols and Covariant Differentiation
Introduction, Christoffel Symbols, Transformation Laws for Christoffel Symbols, Equation of a Geodesic, Affine Parameter, Geodesic Coordinate System, Covariant Differentiation, Rules for Covariant Differentiation, Some Useful Formulas, Intrinsic Derivative: Parallel Transport, Alternative Derivation of Equation of Geodesic, Exercises
The Riemann Curvature Tensor
Introduction, The Riemann Curvature Tensor, Commutation of Covariant Derivative: Another Way of Defining the Riemann Curvature Tensor, Covariant form of the Riemann Curvature Tensor, Properties of the Riemann Curvature Tensor, Uniqueness of Riemann Curvature Tensor, Number of Algebraically Independent Components of the Riemann Curvature Tensor, The Ricci Tensor and the Scalar Curvature, The Einstein Tensor, The Integrability of Riemann Tensor and the Flatness of the Space, Einstein Space, Curvature of a Riemannian Space, Spaces of Constant Curvature, Exercises
Some Advanced Topics
Introduction, Geodesic Deviation, Decomposition of Riemann Curvature Tensor, Electric and Magnetic Parts of the Riemann and Weyl Tensors, Classification of Gravitational Fields, Invariants of the Riemann Tensor, Lie Derivative, The Killing Equation, The Curvature Tensor and Killing Vectors, Curvature Tensors Involving Riemann Tensor, Exercises
Applications
Introduction, Maxwell’s Equations, Special Coordinate System, Energy-momentum Tensors, Kinematical Quantities—Raychaudhuri’s Equation, Solutions of Einstein Field Equations, Some Important Tensors
Bibliography
Answers and Hints to Exercises
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