COURSE GOALS:
Introducing basic concepts of general theory of relativity, learning to use tensor calculus in curved space.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
3. MAKING JUDGEMENTS
3.1 work with a high degree of autonomy, even accepting responsibilities in project planning and in the managing of structures
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
5.3 carry out research by undertaking a PhD
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the course, students will be able to:
* List and explain basic assumptions of general relativity;
* Do calculations involving tensors in curved spaces;
* Quantitatively describe motion of particle in a gravitational field;
* Quantitatively describe the influence of gravitational field to physical processes, apply to the dilatation of time in gravitational field;
* Use Einstein equation to quantitatively describe the gravitational field of spherically symmetric sources of gravitation;
* List and explain the singularities of the spherically symmetric solution;
* List the main experimental tests of general theory of relativity;
COURSE DESCRIPTION:
Reviewing special relativity, 4-vectors, invariants (3 hours)
Gauss' theorem; principle of minimal action for fields (3 hours)
Basic concepts of general theory of relativity, the equivalence principle, curved spaces, metric (3 hours)
Tensors in curved space(time) (3 hours)
Parallel displacement (3 hours)
Motion of particles in gravitational field (3 hours)
Newton's limit. Gravitational redshift. (3 hours)
Properties of Riemann tensor (3 hours)
Parallel displacement around closed curves (3 hours)
Einstein's equation (3 hours)
Action principle for general theory of relativity (3 hours)
Schwarzschild metric (3 hours)
Black holes (3 hours)
Energy momentum tensor, Birkhoff's theorem (3 hours)
Experimental tests of general theory of relativity (3 hours)
REQUIREMENTS FOR STUDENTS:
Students are required to pass written exam at the end of the semester.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Students who passed the written exam are allowed to take oral exam. Students who attended lectures regularly and were active in solving problems may be exempted from the oral part of the exam.
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