Relativity Theory

Course FSI3035 (7.5hp)

Teachers: Konstantin Zarembo, Alexander Krikun

Schedule

Lecture 1
Tuesday, October 22, 13:15-15:00 (FB51)
Lecture 2
Thursday, October 24, 13:15-15:00 (FB51)
Lecture 3
Tuesday, October 29, 13:15-15:00 (FA31)
Lecture 4
Wednesday, October 30, 13:15-15:00 (FB51)
Lecture 5
Friday, November 1, 13:15-15:00 (FB41)
Lecture 6
Tuesday, November 5, 13:15-15:00 (FB51)
Lecture 7
Wednesday, November 6, 13:15-15:00 (FA31)
Lecture 8
Monday, November 11, 15:15-17:00 (FA31)
Lecture 9
Tuesday, November 12, 13:15-15:00 (FB51)
Lecture 10
Wednesday, November 13, 15:15-17:00 (FB51)
Lecture 11
Tuesday, November 19, 13:15-15:00 (FB51)
Lecture 12
Wednesday, November 20, 13:15-15:00 (FA32)
Lecture 13
Friday, November 22, 13:15-15:00 (FA31)
Lecture 14
Wednesday, December 4, 13:15-15:00 (FB54)
Lecture 15
Friday, December 6, 13:15-15:00 (FA31)

Assignment 1
pdf
Assignment 2
pdf
Assignment 3
pdf
Assignment 4
pdf
Assignment 5
pdf
Assignment 6
pdf

Course Plan

  1. Introduction
    1. Equivalence principle (1.2.1, 3.2)
    2. Recap of special relativity (2.3.3, 10.2)
  2. Geometry
    1. Curvilinear coordinates (4.2, 11.1.1)
    2. Tensor calculus (11.1.1)
    3. Covariant differentiation (11.1.2, 11.1.3, 11.2.1)
    4. Curvature (4.3.3, 11.3)
  3. Particle in gravitational field
    1. Twin paradox and action principle in Special Relativity (A.1)
    2. Geodesic motion (4.2.1, 5.2, 11.2.2, 12.1.1)
  4. Einstein's equations
    1. Conservation laws and continuity equation (10.3.2)
    2. Energy-momentum tensor (10.4)
    3. Einstein's equations (12.2)
    4. Newton's constant, Planck mass and the cosmological constant (12.4.3)
  5. Black holes
    1. Schwarzschild solution of Einstein's equations (6.1.1, 12.3)
    2. Event horizon (6.4.1, 6.4.3)
    3. Celestial mechanics (6.3)
    4. Planetary orbits in GR (6.4.4)
    5. Falling into black hole (6.4.2, 6.4.3)
  6. Cosmology
    1. Hubble law (7.1.1, 7.1.2, 7.1.3)
    2. Friedmann-Robertson-Walker metric (7.3)
    3. Friedmann equations (12.4.2, 8.1)
    4. Big Bang (8.2)
    5. Brief history of the Universe (8.3.2)
  7. Physical processes in the expanding Universe
    1. Thermal history (8.3.1, 8.3.2)
    2. Expansion rate and age of the Universe (8.2)
    3. Neutrino decoupling (8.5.3)
    4. Nucleosynthesis (8.4)
    5. Recombination (8.5.1)
    6. Jeans instability and structure formation (9.2.3)

The numbers in brackets indicate sections in the textbook

The course will losely follow this book, but any other textbook that covers similar material would do. Here is a small selection of somewhat more advanced introductory books on General Relativity and Cosmology:

Problem Set: Problems