General relativity

Lecturer:

Oldřich Semerák (gar.)

Tutor:

Oldřich Semerák (gar.)

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 Einstein equations and black holes. General relativity in astrophysics and cosmology: relativistic stellar models, final stages of stellar evolution; Friedmann's cosmological models.

Requirements:

02TEF2, 02GMF1

Syllabus of lectures:

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

2. Equivalence principle. General covariance (general relativity) principle.

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

4. Covariant derivative.

5. Riemann curvature tensor. Ricci tensor and scalar curvature.

6. Einstein´s gravitational law.

7. Schwarzschild´s solution of Einstein equations.

8. Schwarzschild black hole - horizon, singularity.

9. Black holes. Kerr´s solution of Einstein equations. Gravitational collapse.

10. Astrophysical aspects of black holes.

11. Relativistic stellar models.

12. Fundamentals of relativistic cosmology.

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] Dvořák L.: General Relativity Theory and Modern Physical View of the Universe (in Czech), SPN, Praha 1984

Recommended references:

[2] P. Hájíček: An introduction to the relativistic theory of gravitation, Springer, Berlin 2008Recommended references:

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: