Obecná teorie relativity / General theory of relativity


doc. RNDr. Oldřich Semerák, DSc.

spring term 2022, 3/0 exam

Short syllabus:

Fundamental principles of general theory of relativity; principle of equivalence, principle of general covariance. Parallel transport. Geodesics. Time dilation and frequency shift in a gravitational field. Covariant derivative. Curvature, the Riemann tensor. Energy-momentum tensor (ideal fluid). Einstein field equations. Lie derivative and space-time symmetries. Schwarzschild solution of Einstein's equations. Homogeneous and isotropic cosmological models.

Introductory course of general theory of relativity. The only specific knowledge assumed is the real four-dimensional tensor formalism (namely the abstract-index formalism) -- the same we were using in the special-relativity course. It is not necessary to know differential geometry in advance, we will introduce the necessary notions along the way.

Follow-ups of this subject are the courses NTMF037 – Relativistic physics  I (in fall term) and NTMF038 – Relativistic physics  II (in spring term).

Time, space, rules:

Thursday 10:40-12:55, T1 lecture room (MFF Trója).

In 2021/22, the course is being taught live in Czech, with streming switched on (but not recorded) ... link: https://www.mff.cuni.cz/cs/verejnost/multimedia/t1-stream. Videos from 2020/21 English run are linked below. (Please note there is also an "official" recording in Czech at Faculty webpages https://is.mff.cuni.cz/prednasky.)
Examinantion in Czech as well as in English may be chosen. Any feedback welcome (email: oldrich.semerak@mff.cuni.cz).


lecture notes: Relativistic Physics (first 13 chapters)
Misner, Thorne & Wheeler: Gravitation
Dvořák: Obecná teorie relativity a moderní­ fyzikální­ obraz vesmíru (skripta)

Links to recordings from 2020/21 run (mp4):

Fundamental principles

Parallel transport


Time dilation and frequency shift


Riemann tensor; Ideal fluid

Hydrostatic equilibrium; Einstein field equations

Einstein equations; Principle of minimal coupling

Introduction -- popular summary of GR

Lie derivative and space-time symmetries

Schwarzschild metric

Geodesic motion in Schwarzschild field

Cosmology -- FLRW metrics, cosmic fluid

Cosmological redshift; Friedmann equation and cosmic evolution