General Theory of Relativity

  1. Review of special relativity: geometry of Minkowski spacetime.
  2. Crash course of differential geometry: differential manifolds, vetors and tensors, connection, curvature.
  3. Equivalence principle and postulates of Einstein's theory of gravity.
  4. Einstein's equations and their basic properties.
  5. Schwarzschild solution: motion of test particles, bending of light, black holes.
  6. Cosmological solutions: Friedman-Robertson-Walker metrics (cosmological redshift, big bang, horizons).
  7. Gravitational waves: linearized gravity, generation of gravitational waves and their detection.

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