General Theory of Relativity

Course guarantor:

Boris Tomášik

Lecturer:

Boris Tomášik

Tutor:

Tomáš Poledníček

Supervisor:

Department of Physics

Synopsis:

The goal is to learn the basics of General Relativity theory as well as its applications, mainly in cosmology. The students will get acquainted with the starting points of General Relativity. The course includes the explanation of necessary mathematics: differential geometry. Classic results are derived, like the precession of Mercury, gravitational frequency shift and gravitational bending of light. The participants learn about Schwarzschild metrics and its solution leading to black holes. In the application part the Friedman-Robertson-Walker metrics is introduced and dynamics of the Universe is discussed.

Requirements:

Syllabus of lectures:

1.Starting points of general relativity, Einstein equivalence principle, Locally Inertial Frames

2.Curved spaces in more dimensions, Riemann spaces, metrics, tensors, geodetics

3.Riemann tensor, energy-momentum tensor, Einstein equations

4.Schwarzschild metrics, Birkhoff theorem, geodesics and photon trajectory in Schwarzschild metrics

5.Experimental tests of general relativity: gravitational frequency shift, precession of Mercury, gravitational light bending, gravitational lenses

6.Black holes

7.Rotating black holes

8.Gravitational waves

9.Friedman-Robertson-Walker metrics

10.Cosmological models

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] M.P. Hobson, G.P. Efstathiou, A.N. Lasenby: General Relativity, An Introduction for Physicists, Cambridge UP, Cambridge, 2006

[2] R.H. Price: General Relativity Primer, American Journal of Physics 50 (1982) 300

Recommended references:

[3] W. Rindler: Relativity (Special, General, and Cosmological), 2 edition, Oxford University Press, New York, 2006

[4] L. Ryder: Introduction to General Relativity, Cambridge UP, Cambridge, 2009

[5] A. Zee, Einstein Gravity in a Nutshell, Princeton University Press, 2013

[6] K. Kuchař, Základy obecné teorie relativity, Academia, Praha, 1968

[7] G. t’Hooft: Introduction to General Relativity, Rinton Press, Princeton, 2001

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomBR:10 Tomášik B. 18:00–19:50 (lecture parallel1) Břehová 7
Thu	roomBR:115 Poledníček T. 16:00–17:50 (parallel nr.101) Břehová 7
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Jaderná a částicová fyzika (compulsory elective course)