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Krishna's Theory of Relativity, Edition-31B
CONTENTS- THEORY OF RELATIVITY, Chapter 1: Classical Theory of Relativity: Speed of Light 1. Introduction 2. Inertial Frame (Galilean Frame) 3. Galilean Transformations 4. Fictitious Force 5. Electrodynamics 6. Fizeau's Experiment 7. Michelson and Morley Experiment 8. Explanation of Negative Results (Null Results) Chapter 2: Lorentz Transformations 1. Introduction 2. The New Concept of Space and Time 3. Postulates of Special Theory of Relativity 4. Lorentz Transformation Equations 5. Consequences of Lorentz Transformations 6. Time Dilation or Apparent Retardation of Clocks 7. An Interesting Example of Time Dilation 8. Experimental Verification on Time Dilation 9. Simultaneity 10. Relativistic Formulae for Composition of Velocities 11. Relativistic Formulae for Composition of Accelerations 12. Relativity of Time: Proper Time 13. Lorentz Transformation Form a Group 14. Aberration (Relativistic Treatment) 15. Doppler's Effect 16. Confirmation of Doppler Effect Chapter 3: Relativistic Mechanics 1. Mass and Momentum 2. Newton's Laws of Motion 3. Measurement of Different Units 4. Experimental Verification of the Relation 5. Transformation Formula for Mass 6. Transformation Formula for Momentum and Energy 7. Particle with Rest Mass Zero 8. Binding Energy 9. Transformation Formula for Force 10. Relativistic Transformation Formula for Density 11. Minkowski Space (Four Dimensional Continuum) 12. Geometrical Interpretation of Lorentz Transformation 13. Space and Time Like Intervals 14. World Points and World Lines 15. Light Cone 16. Proper Time 17. Energy Momentum Four Vector 18. Four Vector (World Vectors) 19. Relativistic Equations of Motion 20. Minkowski's Equation of Motion Chapter 4: Special Relativity in Classical Mechanics 1. Introduction 2. Lorentz Transformation 3 Relativistic Lagrangian and Hamiltonian Chapter 5: Tensor Calculus Part-1 Tensor and Line Element 1. Summation Convention 2. Dummy Suffix 3. Real Suffix 4. Kronecker Delta 5. Determinant 6. Four Vectors (World Vectors) 7. Transformation of Co-ordinates 8. Tensor 9. Symmetric Tensor 10. Anti-symmetric Tensor 11. Addition of Tensor 12. Inner Product of Two Vectors 13. Multiplication of Tensors 14. Contraction 15. Reciprocal Symmetric Tensor 16. Relative Tensor 17. Riemannian Metric 18. Associate Tensors 19. Magnitude of a Vector 20. Angle between Two Vectors Part-2 Geodesic Curves, Covariant Differentiation 21. Christoffel Symbols 22. Geodesic 23. Covariant Differentiation of Tensor 24. Gradient of a Scalar 25. Derived Vector ??Projection 26. Tendency of Vector 27. Curl of a Vector 28. Divergence of a Vector 29. Parallel Displacement of Vectors 30. Principal Normal 31. Geodesic Co-ordinates 32. Natural Co-ordinates Part-3 Curvature Tensor 33. Riemannian Christoffel's Tensor 34. Covariant Curvature Tensor 35. Flat Space Time 36. Space of Constant Curvature Chapter 6: The General Theory of Relativity 1. Introduction of General Theory of Relativity 2. Principle of Covariance 3. Principle of Equivalence 4. Mach’s Principle 5. Hypothesis and Postulates of General Relativity Chapter 7: Relativistic Field Equations 1. Energy Momentum Tensor Chapter 8: Schwarzschild Solution 1. Relation between M and m, Isotropic co-ordinates 2. Crucial Tests in General Relativity Chapter 9: Cosmology 1. Cosmological Models 2. Weyl Theory 3. Hubble’s Law in Cosmology Chapter 10: Electrodynamics 1. Introduction (Maxwell's Equations) 2. Gauge Transformation 3. Lorentz Condition 4. Electromagnetic Energy Momentum Tensor 5. Energy and Momentum of the Electro-Magnetic Field 6. Electromagnetic Stress