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).
Monday 14:00-18:50, with a few breaks, at T1 lecture room (MFF Trója).
In 2023/24, the course is being taught in Czech (or according to the audience), with online stream possibly provided. 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 may be chosen.
Please, contact me by email in case you needed anything (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]
... Vít Anderle (October 9)
... notes by Vít
... 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]
... Štěpán Kasáček (October 16)
... 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)]
... Marek Jankola (October 23)
... properties of the FW transport in detail, spin-behaviour derivation is not compulsory
4) Uniqueness of the Riemann tensor
[Kuchař, section II.5.8]
... Matyáš Bílek (October 30)
... understanding required, without details (transformations)
5) Equivalent criteria for space-time flatness
[Kuchař, section II.6]
... Martin Odehnal, Jakub Smorada (November 6)
... 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]
... Alžběta Maleňáková (November 13)
... examined almost in detail (final tricks are not compulsory)
7) Electro-geodesics in the Kerr-Newman space-time, Carter equations
[GTR, section 17.3]
... Samuel Brož (November 20)
... 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]
... Tomáš Trachta, David Kománek (November 27)
... 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]
... Michal Stratený (December 4)
...
notes by Michal
... examined in detail
10) Asymptotic form of the field of an isolated source
[Bičák, Rudenko, section 3.2]
... Jan Masák (December 11)
... should just know what it is about
11) Wave-fronts in field theories
[Bičák, Rudenko, section 4.1]
... Jakub Sanitrák (December 18)
...
notes by Jakub
... may be examined in semi-detail
12) Example of a gravitational wave in an exact theory (sandwich wave)
[Bičák, Rudenko, section 4.2]
... Josef Fruhauf (January 8)
... may be examined in semi-detail
13) (possibly) Thermodynamics, hydrodynamics, electrodynamics, geometrical optics, and kinetic theory
[MTW, section 22]
... Poula Tadros (January 8 ... will see...)
... should know basic equations in GR setting
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
