Announcements:

• (1/11) Reformulated exercise-7 in note-3 after a question from the audience.
• (14/10) Week 42 (14-18/10) is a "skemafri uge" -- no teaching this week.
• (19/8) There will be no teaching in the week 36 (September 4th).
• (19/8) First meeting: August 28th.

Schedule:

Plan:

1. [pdf] Introduction. Special relativity. Relativistic kinematics. (19.08.21)
   Event; Distance; Space; Metric; Space-time; Inertial frame of reference; Space-time interval; Euclidean and pseudo-Euclidean metric; Lorentz transformation; Special principle of relativity; Least action principle; Relativistic action of a massive body; Canonical momentum; Relativistic momentum and energy of a massive body.
2. [pdf] Equivalence principle. (19.08.21)
   Inertial forces; Equivalence principle; Curved spacetime; Geometric theory of gravitation; General principle of relativity; Principle of general covariance.
3. [pdf] Vectors in curvilinear coordinates. Covariant differentiation. (19.08.21)
   Covariant and contravariant vectors; Tensors; Implicit summation; Metric tensor; Covariant differential; Christoffel symbols;
4. [pdf] Motion of free particles in curved spaces. Geodesics. (19.08.21)
   General covariance; Geodesic; Gravitational potential; Null geodesic.
5. [pdf] Electrodynamics in curved spaces. (19.08.21)
   Principle of stationary action; Action of charges in electromagentic field; Covariant volume element; Action of electromagentic field; Lorentz force equation in gravitational fields; Maxwell equations in gravitational fields.
6. [pdf] Action of matter in general relativity. (19.08.21)
   Action of matter in general relativity; Stress-energy-momentum tensor of matter; Stress-energy-momentum conservation law;
7. [pdf] Action of gravitation. Gravitational field equation. (19.08.21)
   Riemann tensor; Ricci tensor; Ricci scalar; Einstein equation; Hilbert-Einstein action;
8. [pdf] Newtonian limit of general relativity. Gravitational waves. (19/08/21)
   Newtonian limit; Gravitational waves.
   
9. [pdf] Schwarzschild solution. Motion in the Schwarzschild metric. (19/08/21)
   Schwarzschild coordinates; Schwarzschild solution.
10. [pdf] Classical tests of GTR (19/08/21)
    Anomalous perihelion shift; Bending of light; Gravitational red-shift.
11. [pdf] Radial fall in the Schwarzschild metric. (19/08/21)
    Lemaitre coordinates. Coordinate singularity. Gravitational singularity. Event horizons. Black holes.
12. [pdf] Geometry in a homogeneous and isotropic universe. Friedmann equation. (19.08.21)
    Space with constant curvature; Friedmann-(Lemaitre-Robertson-Walker) metric; Friedmann equation.
    
13. [pdf] Solutions to Friedman equation. Big Bang. Cosmological red-shift. Hubble constant. (19.08.21)
    Big Bang; Hubble constant; cosmological red-shift; cosmological constant; radiation-, matter-, and dark-energy-dominated universe.
14. [pdf] Proper time and length intervals in general relativity. (19.08)
    

1. Gerard 't Hooft, Introduction to General Relativity [500kB PDF file], Rinton Press, Inc., Princeton NJ, ISBN 1-58949-000-2.
2. A. Einstein, Relativity: The Special and General Theory [600kB PDF file];
3. Warren Siegel, Fields, http://arxiv.org/abs/hep-th/9912205, [1215kB PDF file].