More on geometry: tensor densities, covariant divergence, Fermi-Walker transport. Invariant and coordinate features of the Schwarzschild solution, analytic extension of the metric. Pericentre precession and light bending in the Schwarzschild field. Reissner-Nordström solution of the Einstein equations. Kerr and Kerr-Newman solutions of the Einstein equations, Carter equations for electro-geodesic test motion. Gravitational collapse and black holes: black-hole uniqueness theorems, formation of black holes, laws of black-hole (thermo)dynamics, extraction of energy from black holes. Relativistic theory of stellar equilibria: description of a static and spherically symmetric star, equations of stellar equilibria, radial oscillations and stability. Final stages of stellar evolution: degenerate fermion gas, white dwarfs and neutron stars; Chandrasekhar limit. Linearized theory of gravitation, plane gravitational waves.

A follow-up of the basic general-relativity course (NTMF111), mainly suitable for theoretical physicists and astrophysicists at the turn of their bachelor and master studies.

The course continues by NTMF038 – Relativistic physics II (in spring term).

Thursday 13:10-18:00, with a few breaks, at T1 lecture room (MFF Trója).

In 2021/22, the course is being taught live and in Czech (videos from 2020/21 English run are linked below).

Student seminar talks: one talk per year (per 2 semesters of Relativistic physics) is generally required for credit.

Examinantion in Czech as well as in English can be chosen.

Comments welcome during lecture or via email (oldrich.semerak@mff.cuni.cz).

1) Composition of Lorentz transformations, boosts and Thomas precession
[Votruba, sections IV.7 and IV.8; also GTR, section 18.2]

... Kateřina Mladá (07-10)

... you should know "in principle", examined without details

2) Parallel transport (derived in a different way than in the first semester)
[Kuchař, section II.4]

... Jan Došek (14-10)

... examined, but not in full detail

3) Angular momentum (spin) and the Fermi-Walker transport
[Bičák, Rudenko, sections 1.5, 1.6, 2.2; also GTR, chapter 18 (up to 18.1)]

... Jan Kříž, Róbert Jurčo (04-11)

... properties of the FW transport in detail, spin-behaviour derivation is not compulsory

4) Uniqueness of the Riemann tensor
[Kuchař, section II.5.8]

... Eliška Klimešová (21-10)

... understanding required, without details (transformations)

5) Equivalent criteria for space-time flatness
[Kuchař, section II.6]

... Alžběta Maleňáková (11-11)

... examined almost in detail (tricks in computation of "the integral" are not compulsory)

6) Pericentre shift, light bending
[GTR, section 17.1; or also Dvořák]

... Jan Šenk (18-11)

... examined almost in detail (final tricks are not compulsory)

7) Electro-geodesics in the Kerr-Newman space-time, Carter equations
[GTR, section 17.3]

... Barbora Adamcová (25-11)

... examined in semi-detail (need not learn the metric by heart)

8) Linearized theory of gravitation
[Bičák, Rudenko, section 3.1; or GTR, sections 22.1-22.4]

... Michael Vávra (02-12)

... examined in detail

9) Plane waves in the linearized gravity
[Bičák, Rudenko, sections 3.3 and 3.4; or GTR, sections 22.5 and 22.6]

... Róbert Jurčo, Monika Dubová (09-12)

... examined in detail

10) Asymptotic form of the field of an isolated source
[Bičák, Rudenko, section 3.2]

... Tomáš Faikl, Kamil Mudruňka, Milan Vrána (16-12)

... should just know what it is about

11) Wave-fronts in field theories
[Bičák, Rudenko, section 4.1]

... Jáchym Baláž (06-01)

... may be examined in semi-detail

12) Example of a gravitational wave in an exact theory (sandwich wave)
[Bičák, Rudenko, section 4.2]

... David Kramár, Vít Beneš (will see when)

... may be examined in semi-detail

13) Thermodynamics, hydrodynamics, electrodynamics, geometrical optics, and kinetic theory
[MTW, section 22]

... Martin Crhán (will see when)

... should know basic equations in GR setting

References:

GTR: Relativistic Physics

Votruba: Základy speciální teorie relativity

Kuchař: Základy obecné teorie relativity

Bičák, Rudenko: Teorie relativity a gravitační vlny (skripta)

Dvořák: Obecná teorie relativity a moderní fyzikální obraz vesmíru (skripta)

Misner, Thorne & Wheeler: Gravitation

(Kuchař, Bičák & Rudenko, and MTW we have as files, can send you.)

5th October morning, 5th October afternoon

12th October morning, 12th October afternoon, 12th October afternoon, Boosts & Thomas precession

19th October morning, 19th October afternoon, Lie derivative & Killing vectors, and, if you did not recognize what I had on T-shirt

26th October lecture, Parallel transport

2th November lecture, Spin and Fermi-Walker transport

9th November lecture, Uniqueness of the Riemann tensor

16th November lecture, Equivalent criteria of flatness, Apsidal precession & light bending

23th November lecture, Motion in Kerr-Newman (Carter equations), and dark side of the T-shirt

30th November lecture, Linearized theory of gravitation

7th December lecture, Plane waves in linearized theory

14th December lecture, Asymptotic form of an isolated-system field (multipole expansion)

Wave-fronts in field theories,
Xmas climbing (contains upsetting scenes!),
and
"Nesem vám noviny" (Silvester-Eve edit)

singing of carols via Zoom was not recorded, but we made it, even with a decent piano accompaniment

4th January -- Chandrasekhar limit, Sandwich wave in exact theory, Non-gravitational physics within GR

I made a mistake in one of the lectures (second part of the semester). I mean quite a serious one, not just a wrong index :-(. Who discovers and explains it will be rewarded somehow (don't know how yet).