General Relativity

1. Key Concepts
   1. Spacetime
      1. Curvature
         1. Impact of mass and energy on spacetime curvature
         2. Visualizing curved spacetime
         3. Mathematical description using Riemannian geometry
      2. Geodesics
         1. Definition as the shortest path in curved spacetime
         2. Role in describing free-fall motion
         3. Examples in gravitational fields
      3. Coordinate systems in general relativity
         1. Local versus global reference frames
         2. Commonly used coordinate systems: Schwarzschild, Kerr, and flat-space coordinates
         3. Transformation between different coordinate systems
   2. Equivalence principle
      1. Weak equivalence principle (universality of free fall)
         1. Historical experiments confirming the principle, e.g., Galileo, Eötvös experiment
         2. Role in developing the theory of general relativity
      2. Strong equivalence principle
         1. Implications for physics in accelerating frames
         2. Relationship with local Lorentz invariance and local position invariance
   3. Gravitational time dilation
      1. Concept of time running at different rates in different gravitational potentials
      2. Mathematical description using the metric tensor
      3. Implications for high-precision technologies, e.g., GPS systems
   4. Redshift and blueshift
      1. Gravitational redshift
         1. Impact on the wavelength of light escaping a gravitational field
         2. Classic experiments, e.g., Pound-Rebka experiment
      2. Doppler shift in an expanding universe
         1. Cosmological redshift as evidence for expanding universe
         2. Applications in astronomy and the study of distant galaxies
      3. Gravitational blueshift
         1. Phenomenon occurring when light enters a stronger gravitational field
         2. Detection and measurement challenges
   5. Light deflection
      1. Prediction of light bending near massive objects
      2. Observational evidence, e.g., Eddington's 1919 solar eclipse experiment
      3. Applications in cosmology and astrophysics, such as gravitational lensing
   6. Frame-dragging
      1. Concept and prediction by general relativity
      2. Rotational effects of massive, spinning bodies on the spacetime around them
      3. Detecting frame-dragging through experiments like the Gravity Probe B mission
      4. Lense-Thirring effect and its implications for astrophysical phenomena