General Relativity

Garant předmětu:

Boris Tomášik

Lecturer:

Oldřich Semerák

Tutor:

Supervisor:

Department of Physics

Synopsis:

Introduction to general theory of relativity: principle of equivalence and principle of general covariance, parallel

transport and geodesic equation, gravitational redshift. Curvature and Einstein's gravitational law. Schwarzschild solution of the Einstein equations, homogeneous and isotropic cosmological models.

Requirements:

02TEF2, 02GMF1

Syllabus of lectures:

1. Theory of gravitation and physical picture of the world.

2. Equivalence principle. Principle of general covariance.

3. Parallel transport and equation of geodesic; affine connection.

4. Gravitational shift of frequency.

5. Covariant derivative.

6. Riemann curvature tensor and its meaning, Ricci tensor and scalar.

7. Einstein ́s equations of the gravitational field.

8. Schwarzschild solution of Einstein equations.

9. Fundamentals of relativistic cosmology – homogeneous and isotropic cosmological models.

Syllabus of tutorials:

Study Objective:

Knowledge:

Learn the fundamentals of contemporary gravitation theory.

Skills:

Solving simple examples from gravitaion theory.

Study materials:

Key references:

[1] C. Bambi, Introduction to General Relativity, Springer Verlag, Singapore 2018

[2] M. Blecher, General Relativity: A First Examination, World Scientific Publishing 2016

[3] P. Hájíček: An Introduction to the Relativistic Theory of Gravitation, Springer Verlag, Berlin 2008

Recommended references:

[3] Schutz B.: A First Course in General Relativity, 2nd ed. (Cambridge Univ. Press, Cambridge 2009)

[4] Stephani H.: Relativity: An Introduction to Special and General Relativity, 3rd ed. (Cambridge Univ. Press, Cambridge 2004)

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (elective course)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization, elective course)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (elective course)
• BS Informatická fyzika (elective course)
• BS Aplikace softwarového inženýrství (elective course)
• BS Aplikovaná informatika (elective course)
• BS jaderné inženýrství B (elective course)
• BS Jaderné inženýrství C (elective course)
• BS Dozimetrie a aplikace ionizujícího záření (elective course)
• BS Experimentální jaderná a částicová fyzika (elective course)
• BS Inženýrství pevných látek (elective course)
• BS Diagnostika materiálů (elective course)
• BS Fyzika a technika termojaderné fúze (elective course)
• BS Fyzikální elektronika (elective course)
• BS Jaderná chemie (elective course)
• Matematické inženýrství - Matematická fyzika (PS)