Einstein in Matrix Form

Exact Derivation of the Theory of Special and General Relativity without Tensors

• Special Relativity
  • Galilei Transformation
    • Relativity Principle of Galilei
    • General Galilei Transformation
    • Maxwell’s Equations and Galilei Transformation
    • Simultaneity at Different Places
  • Lorentz Transformation
    • Introduction
    • Determining the Components of the Transformation Matrix
    • Simultaneity at Different Places
    • Length Contraction of Moving Bodies
    • Time Dilation
  • Invariance of the Quadratic Form
    • Invariance with Respect to Lorentz Transformation
    • Light Cone
    • Proper Time
  • Relativistic Velocity Addition
    • Galilean Addition of Velocities
  • Lorentz Transformation of the Velocity
  • Momentum and Its Lorentz Transformation
  • Acceleration and Force
    • Acceleration
    • Equation of Motion and Force
    • Energy and Rest Mass
    • Emission of Energy
  • Relativistic Electrodynamics
    • Maxwell’s Equations
    • Lorentz Transformation of the Maxwell’s Equations
    • Electromagnetic Invariants
    • Electromagnetic Forces
  • The Energy–Momentum Matrix
    • The Electromagnetic Energy–Momentum Matrix
    • The Mechanical Energy–Momentum Matrix
    • The Total Energy–Momentum Matrix
  • The Most Important Definitions and Formulas in Special Relativity
• Theory of General Relativity
  • General Relativity and Riemannian Geometry
  • Motion in a Gravitational Field
    • First Solution
    • Second Solution
    • Relation Between ˜Γ and G
  • Geodesic Lines and Equations of Motion
    • Alternative Geodesic Equation of Motion
  • Example: Uniformly Rotating Systems
  • General Coordinate Transformations
    • Absolute Derivatives
    • Transformation of the Christoffel Matrix ˜Γ .
• Gravitation of a Spherical Mass
• Appendix A – Vectors and Matrices
• Appendix B – Some Differential Geometry
• Appendix C – Geodesic Deviation
• Appendix D – Another Ricci-Matrix