General Relativity

Tensors and curvature through gravitational radiation, cosmology and black holes.

Syllabus

  1. Lectures

    1. 1. Introduction and the geometric viewpoint on physics.
    2. 2. Introduction to tensors.
    3. 3. Tensors continued.
    4. 4. Volumes and volume elements; conservation laws.
    5. 5. The stress energy tensor and the Christoffel symbol.
    6. 6. The principle of equivalence.
    7. 7. Principle of equivalence continued; parallel transport.
    8. 8. Lie transport, Killing vectors, tensor densities.
    9. 9. Geodesics.
    10. 10. Spacetime curvature.
    11. 11. More on spacetime curvature.
    12. 12. The Einstein field equation.
    13. 13. The Einstein field equation (variant derivation).
    14. 14. Linearized gravity I: Principles and static limit.
    15. 15. Linearized gravity II: Dynamic sources
    16. 16. Gravitational radiation I
    17. 17. Gravitational radiation II
    18. 18. Cosmology I
    19. 19. Cosmology II
    20. 20. Spherical compact sources I
    21. 21. Spherical compact sources II
    22. 22. Black holes I
    23. 23. Black holes II