General Theory of Relativity or the theory of relativistic gravitation is the one which describes black holes, gravitational waves and expanding Universe. The goal of the course is to introduce you into this theory.

The introduction is based on the consideration of many practical generic examples in various scopes of the General Relativity. After the completion of the course you will be able to solve basic standard problems of this theory. We assume that you are familiar with the Special Theory of Relativity and Classical Electrodynamics. However, as an aid we have recorded several complementary materials which are supposed to help you understand some of the aspects of the Special Theory of Relativity and Classical Electrodynamics and some of the calculational tools that are used in our course.

Syllabus

Week 1: General Covariance

Week 2: Covariant differential and Riemann tensor

Week 3: Einstein-Hilbert action and Einstein equations

Week 4: Schwarzschild solution

Week 5: Penrose-Carter diagrams

Week 6: Classical tests of General Theory of Relativity

Week 7: Interior solution and Kerr’s solution

Week 8: Collapse into black hole

Week 9: Gravitational waves

Week 10: Gravitational radiation

Week 11: Friedman-Robertson-Walker cosmology

Week 12: Cosmological solutions with non-zero cosmological constant

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