Relativity Theory
Course FSI3035 (7.5hp)
Teachers: Konstantin Zarembo, Alexander Krikun
Schedule
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Lecture 1
- Tuesday, October 22, 13:15-15:00 (FB51)
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Lecture 2
- Thursday, October 24, 13:15-15:00 (FB51)
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Lecture 3
- Tuesday, October 29, 13:15-15:00 (FA31)
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Lecture 4
- Wednesday, October 30, 13:15-15:00 (FB51)
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Lecture 5
- Friday, November 1, 13:15-15:00 (FB41)
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Lecture 6
- Tuesday, November 5, 13:15-15:00 (FB51)
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Lecture 7
- Wednesday, November 6, 13:15-15:00 (FA31)
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Lecture 8
- Monday, November 11, 15:15-17:00 (FA31)
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Lecture 9
- Tuesday, November 12, 13:15-15:00 (FB51)
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Lecture 10
- Wednesday, November 13, 15:15-17:00 (FB51)
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Lecture 11
- Tuesday, November 19, 13:15-15:00 (FB51)
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Lecture 12
- Wednesday, November 20, 13:15-15:00 (FA32)
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Lecture 13
- Friday, November 22, 13:15-15:00 (FA31)
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Lecture 14
- Wednesday, December 4, 13:15-15:00 (FB54)
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Lecture 15
- Friday, December 6, 13:15-15:00 (FA31)
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Assignment 1
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pdf
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Assignment 2
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pdf
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Assignment 3
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pdf
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Assignment 4
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pdf
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Assignment 5
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pdf
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Assignment 6
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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)
- Energy-momentum 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)
- Friedmann-Robertson-Walker 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
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Ta-Pei 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:
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D.S. Gorbunov and V.A. Rubakov
Introduction to the Theory of the Early Universe: Hot Big Bang Theory
(World Scientific, 2011).
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I.B. Khriplovich
General Relativity
(Springer, 2005).
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C.W. Misner, K.S. Thorne and J.A. Wheeler
Gravitation
(W.H. Freeman, 1973).
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B.F. Schutz
A First Course in General Relativity
(Cambridge University Press, 2004).
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S. Weinberg
Cosmology
(Oxford University Press, 2008).
Problem Set:
Problems