General Relativity

1. Experimental Evidence and Tests
   1. Historical Overview of Experimental Tests
      1. Early confirmations
         1. Pre-20th century astronomical observations
         2. Einstein’s prediction and initial tests
      2. Post-Einstein developments
   2. Gravitational Lensing
      1. Basics of gravitational lensing
         1. Light path alteration by massive objects
         2. Einstein Ring and lensing arcs
      2. Types of gravitational lensing
         1. Strong lensing
         2. Weak lensing
         3. Microlensing
      3. Observational evidence
         1. First observation during the 1919 solar eclipse
         2. Use in cosmological studies
         3. Identifying dark matter
      4. Applications
         1. Measuring mass of galaxies and clusters
         2. Detecting exoplanets
         3. Cosmic microwave background fluctuations
   3. Perihelion Precession of Mercury
      1. Anomalous precession explained
         1. Newtonian versus relativistic predictions
      2. Historical observations
         1. 19th-century measurements
         2. Explanation by general relativity
      3. Impact on celestial mechanics
         1. Influence on future relativistic models
         2. Verification with other planetary bodies
   4. Gravitational Redshift
      1. Redshift basics
         1. Frequency change in a gravitational field
         2. Contrast with Doppler redshift
      2. Experimental verifications
         1. Pound-Rebka experiment
         2. Measurements with atomic clocks
      3. Astrophysical observations
         1. Spectral analysis of stars and galaxies
      4. Importance in technology
         1. Impact on telecommunications
   5. Time Dilation Experiments
      1. Concept of time dilation in relativity
      2. Atomic clock experiments
         1. Ground-based verification
         2. Airborne and space-based tests (Hafele–Keating experiment)
      3. Applications in technology
         1. Synchronization in the Global Positioning System (GPS)
         2. Satellite communication systems
      4. Comparisons with Special Relativity predictions
   6. Modern Experimental Tests
      1. Advanced technologies and instruments
         1. Laser Interferometer Gravitational-Wave Observatory (LIGO)
         2. Very Long Baseline Interferometry (VLBI)
      2. Precision measurements
         1. Variations in the gravitational field
         2. Studies in different gravitational environments
      3. Ongoing and future experiments
         1. Space-based missions (e.g., LISA, GRACE)
         2. Developments in quantum optics and gravity
   7. Implications and Challenges
      1. Interpreting experimental data
         1. Aligning theoretical predictions with observations
         2. Statistical methods in astrophysical data
      2. Challenges in extreme environments
         1. Black holes and neutron stars
         2. Early universe conditions
      3. Future paths and theoretical predictions
         1. Testing quantum versions of general relativity
         2. Exploring alternative gravitational theories