Theory of Relativity

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