ÚTF ] [ sylaby ] Karolínka ] 

Obecná teorie relativity
General theory of relativity

NTMF111

doc. RNDr. Oldřich Semerák, DSc. 

spring term 2021, 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. 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 (taught in fall term) and NTMF038 – Relativistic physics  II (taught in spring term).

Time, space, rules:

Thursday from 14:00, lecture room T1. In 2021 it was taught in English via Zoom.
Invitation: link
Meeting ID: 998 827 6224
Passcode: 369661

Lectures were recorded, videos are linked at the bottom of this page. If you noticed anything I should delete from the recordings, please tell me.
Feedback during lectures as well as via email (oldrich.semerak@mff.cuni.cz) is welcome in any case.
Examination in Czech as well as in English may be chosen.
Please note that there is a high-quality recording covering all the course (in Czech) at Faculty webpages https://is.mff.cuni.cz/prednasky/.
Konzultace / diskuse v češtině "samozřejmě" -- kdyžtak se prosím ozvěte. 

References:

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

Links to recorded files (mp4):

March 4 (Fundamental principles) 

March 11 (Parallel transport) 

March 18 (Geodesics) 

March 25 (Time dilation and frequency shift) 

April 1 (Curvature) 

April 8 (Riemann; ideal fluid) 

April 15 (conditions for hydrostatic equilibrium; Einstein field equations) 

April 22 (Einstein equations; principle of minimal coupling) 

April 29 (Introduction -- popular summary of GR) 

May 06 (Lie derivative and space-time symmetries) 

May 13 (Schwarzschild solution) 

May 20 (Geodesic motion in Schwarzschild) 

May 27 (Cosmology -- FLRW metrics, cosmic fluid) 

June 3 (cosmological redshift, Friedmann equation and cosmic evolution)