General Relativity

Developed by Albert Einstein, General Relativity is the modern theory of gravitation, which posits that gravity is not a force but a consequence of the curvature of spacetime. In this framework, the distribution of mass and energy warps the four-dimensional fabric of spacetime, and this curvature, in turn, dictates how objects and even light move through it. As a generalization of Special Relativity and a refinement of Newton's law of universal gravitation, it accurately describes large-scale phenomena such as the orbits of planets, the bending of starlight, the existence of black holes, and the propagation of gravitational waves.

1. Foundations of General Relativity
   1. Historical Context and Motivation
      1. Pre-Einsteinian Views of Gravity
         1. Aristotelian Concepts of Natural Motion
         2. Galilean Mechanics and Inertia
         3. Newton's Revolutionary Synthesis
      2. The Need for a New Theory
         1. Observational Anomalies
         2. Theoretical Inconsistencies
         3. The Quest for Unification
   2. Review of Newtonian Gravity
      1. Newton's Law of Universal Gravitation
         1. Mathematical Formulation
         2. Inverse Square Law
         3. Gravitational Constant
      2. Concept of Gravitational Force
         1. Action at a Distance
         2. Gravitational Field Concept
         3. Superposition Principle
      3. Gravitational Potential
         1. Definition and Properties
         2. Equipotential Surfaces
         3. Potential Energy
      4. Limitations of Newtonian Theory
         1. Instantaneous Action at a Distance
         2. Incompatibility with Special Relativity
         3. Failure to Explain Perihelion Precession
         4. Inability to Account for Light Deflection
         5. Problems with Self-Energy
   3. Special Relativity Prerequisites
      1. The Postulates of Special Relativity
         1. Principle of Relativity
         2. Constancy of the Speed of Light
         3. Experimental Foundations
      2. Spacetime Geometry
         1. The Minkowski Spacetime
            1. Four-Dimensional Spacetime
            2. Spacetime Diagrams
            3. World Lines
         2. Spacetime Interval
            1. Invariant Interval
            2. Timelike Intervals
            3. Spacelike Intervals
            4. Lightlike Intervals
         3. Light Cones
            1. Causal Structure
            2. Past and Future Light Cones
            3. Causal Relationships
      3. Relativistic Kinematics
         1. Time Dilation
            1. Moving Clocks Run Slow
            2. Proper Time
            3. Time Dilation Factor
         2. Length Contraction
            1. Moving Objects Contract
            2. Proper Length
            3. Lorentz Contraction Factor
         3. Relativity of Simultaneity
            1. Lack of Absolute Simultaneity
            2. Simultaneity in Different Frames
      4. Relativistic Dynamics
         1. Mass-Energy Equivalence
            1. E=mc² Derivation
            2. Rest Mass Energy
            3. Binding Energy
         2. Relativistic Momentum and Energy
            1. Four-Momentum
            2. Energy-Momentum Relation
            3. Conservation Laws