Relativity Theory
Course FSI3035 (7.5hp)
Teachers: Konstantin Zarembo, Alexander Krikun
Schedule

Lecture 1
 Tuesday, October 22, 13:1515:00 (FB51)

Lecture 2
 Thursday, October 24, 13:1515:00 (FB51)

Lecture 3
 Tuesday, October 29, 13:1515:00 (FA31)

Lecture 4
 Wednesday, October 30, 13:1515:00 (FB51)

Lecture 5
 Friday, November 1, 13:1515:00 (FB41)

Lecture 6
 Tuesday, November 5, 13:1515:00 (FB51)

Lecture 7
 Wednesday, November 6, 13:1515:00 (FA31)

Lecture 8
 Monday, November 11, 15:1517:00 (FA31)

Lecture 9
 Tuesday, November 12, 13:1515:00 (FB51)

Lecture 10
 Wednesday, November 13, 15:1517:00 (FB51)

Lecture 11
 Tuesday, November 19, 13:1515:00 (FB51)

Lecture 12
 Wednesday, November 20, 13:1515:00 (FA32)

Lecture 13
 Friday, November 22, 13:1515:00 (FA31)

Lecture 14
 Wednesday, December 4, 13:1515:00 (FB54)

Lecture 15
 Friday, December 6, 13:1515:00 (FA31)

Assignment 1

pdf

Assignment 2

pdf

Assignment 3

pdf

Assignment 4

pdf

Assignment 5

pdf

Assignment 6

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

TaPei Cheng
Relativity, Gravitation and Cosmology. A Basic Introduction
(Oxford University Press, 2005).
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:

D.S. Gorbunov and V.A. Rubakov
Introduction to the Theory of the Early Universe: Hot Big Bang Theory
(World Scientific, 2011).

I.B. Khriplovich
General Relativity
(Springer, 2005).

C.W. Misner, K.S. Thorne and J.A. Wheeler
Gravitation
(W.H. Freeman, 1973).

B.F. Schutz
A First Course in General Relativity
(Cambridge University Press, 2004).

S. Weinberg
Cosmology
(Oxford University Press, 2008).
Problem Set:
Problems