Announcements:

• [9/10] There will be no teaching the next two weeks (week 42 and week 43). Next lecture should be on 30/10.
• [26/9] Remember to update the attendance table at the wiki page.
• [18/9] Instead of "recommended exercises" thing the non-recommended exercises will be marked "extra" in the lecture notes.
• [8/9] Added "recommended exercises" to the plan.
• [5/9] Exam should be later than 9/1/24.
• [28/8] Go to our "wiki" page at the linke above, upload an image of you (using the "Media Manager" (at the top right corner)) and add a line with your image and your name to the table of attendance.
• [28/8] Any (reasonable) textbook on General Relativity will do for this course. I suggest Gerard 't Hooft "Introduction to General Relativity" – it is short and freely available from 't Hooft's homepage, [500kB PDF file].
• [28/8] The greyed-out items in the Plan below are preliminary.

Schedule:

• Monday, 10:15-13:00, Aud. 1531-219 (D4)

Plan:

1. [pdf] Introduction. Special relativity. Relativistic kinematics. (27/02/24)
   Keywords: Inertial frame of reference; Lorentz transformation; Spacetime; Space-time interval; Metric; Four-vectors; Special principle of relativity; Least action principle and Lagrangian; Canonical momentum and energy; Relativistic action of a massive body; Relativistic momentum and energy of a massive body.
   Recommended exercises: Coordinate transformations between inertial frames form a Lie group; Galilean transformations as a Lie group, galilean law of velocity addition; Lorentz transformations as a Lie group, relativistic law of velocity addition; Relativistic action of a massive body, relativistic momentum and energy;

2. [pdf] Equivalence principle. (27/02/24)
   Inertial forces; Equivalence of inertial and gravitational masses; Equivalence principle; Gravitation as geometry of spacetime; Curved spacetime; General principle of relativity;
   Recommended exercises: Pendulum with m_g≠m; Potential formulation of Newtonian gravitation; Gravitation as geometry of space; Newtonean limit of Nordström's theory; Equivalence principle implies bending of light and gravitational redshift.

3. [pdf] Vectors in curvillinear coordinates. Covariant differentials of tensors in metric spaces. (27/02/24)
   Covariant transformaion of physical quantities under a (general) coordinate transformation; Principle of covariance; Covariant objects: scalars, vectors, tensors; Covariant differentials of tensors; Christoffel symbols in metric spaces;
   Recommended exercises: All except for transformation formula for Christoffel symbols ;)
4. [pdf] Motion of free bodies in curved spaces. Geodesics. (27/02/24)
   General covariance; Geodesics; Null geodesics; Gravitational potential.
   Recommended exercises: All but "geodesics on a sphere".

5. [pdf] Electrodynamics in curved spaces. (27/02/24)
   Principle of stationary action; Action of charges in electromagentic fields; Covariant volume element; Action of the electromagentic field; Lorentz force equation in gravitational fields; Maxwell equations in gravitational fields.

6. [pdf] The source of gravity: the stress-energy-momentum tensor of matter. (27/02/24)
   Action of matter in general relativity; Stress-energy-momentum tensor of matter as the source of gravitation; Stress-energy-momentum conservation law;

7. [pdf] Action of gravitation. Gravitational field equation (Einstein equation). (27/02/24)
   Riemann tensor; Ricci tensor; Ricci scalar; Einstein equation; Hilbert-Einstein action;

8. [pdf] Newtonian limit of general relativity. Gravitational waves. (27/02/24)
   Newtonian limit; Linearized gravity; Gravitational waves in vacuum.

9. [pdf] Schwarzschild solution. Motion in the Schwarzschild metric. (27/02/24)
   Schwarzschild coordinates; Schwarzschild solution; Schwarzschild radius.

10. [pdf] Classical tests of GTR (27/02/24)
    Anomalous perihelion shift; Bending of light; Gravitational red-shift.

11. [pdf] Radial fall in the Schwarzschild metric. (27/02/24)
    Lemaitre coordinates for Schwarzschild solution; Coordinate singularity; Gravitational singularity; Event horizons; Black holes.

12. [pdf] Geometry in a homogeneous and isotropic universe. Friedmann equation. (27/02/24)
    Friedmann universe; Friedmann-(Lemaitre-Robertson-Walker) metric; Friedmann equations.

13. [pdf] Solutions to Friedmann equation. Big Bang. Cosmological red-shift. Hubble-Lemaitre constant. (27/02/24)
    Big Bang; Cosmological red-shift; Hubble (-Lemaitre) law; Cosmological constant; Radiation-, matter-, and dark-energy-dominated universes.

14. [pdf] Proper time and length intervals in general relativity. (27/02/24)
    

1. Gerard 't Hooft, Introduction to General Relativity [500kB PDF file], Rinton Press, Inc., Princeton NJ, ISBN 1-58949-000-2.