More on geometry: Lie derivative and space-time symmetries, 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 9:50-12:05 and 13:10-15:25, at T2 lecture room (MFF Trója).
In 2020/21, the course was taught via the Zoom application.
Invitation:
link
Meeting ID: 998 827 6224
Passcode: 369661
Lectures were recorded, links are given at the bottom of this page. If you noticed anything I should delete from the recordings, please tell me.
Student seminar talks were organized as web presentations. One talk per year (per 2 semesters of Relativistic physics) is generally required for credit.
Feedback via email (oldrich.semerak@mff.cuni.cz) is welcome as well. Examinantion in Czech as well as in English can be chosen.
1) Lorentz transformation with generic velocity direction (="boost"); Composition of Lorentz transformations in orthogonal directions, Thomas precession
[Votruba, sections IV.7 and IV.8]
... Andrej Zymin (12-10)
... you should know "in principle", examined without details
2) Lie derivative and space-time symmetries
[my latex notes]
... Jan Střeleček, Dan Rod (19-10)
... examined in detail
3) Parallel transport (derived in a different way than we did it in the 1st semester)
[Kuchař, section II.4]
... Jana Menšíková (26-10)
... examined, but not in full detail
4) Angular momentum (spin) and the Fermi-Walker transport
[Bičák, Rudenko, sections 1.5, 1.6, 2.2]
... Pavel Šklíba (02-11)
... properties of the FW transport in detail, spin-behaviour derivation is not compulsory
5) Uniqueness of the Riemann tensor
[Kuchař, section II.5.8]
... Jaroslav Chládek (09-11)
... understanding required, without details (transformations)
6) Equivalent criteria for space-time flatness
[Kuchař, section II.6]
... Klára Ševčíková, Stáňa Tázlarů (16-11)
... examined almost in detail (tricks in computation of "the integral" are not compulsory)
7) Pericentre shift, light bending
[my latex notes, possibly Dvořák]
... Lukáš Knob, Jozef Lipták (16-11)
... examined almost in detail (final tricks are not compulsory)
8) Electro-geodesics in the Kerr-Newman space-time, Carter equations
[my latex notes]
... Rudolf Šmolka, Filip Moučka (23-11)
... examined in semi-detail (need not learn the metric by heart)
9) Linearized theory of gravitation
[Bičák, Rudenko, section 3.1]
... Jan Došek, Václav Kubíček (30-11)
... examined in detail
10) Plane waves in the linearized gravity
[Bičák, Rudenko, sections 3.3 and 3.4]
... Magdalena Parýzková, Tereza Lehečková (07-12)
... examined in detail
11) Asymptotic form of the field of an isolated source
[Bičák, Rudenko, section 3.2]
... Jakub Novotný, Richard Ivánek (14-12)
... should just know what it is about
12) Wave-fronts in field theories
[Bičák, Rudenko, section 4.1]
... Lenka Doležalová, Šimon Vedl (21-12)
... may be examined in semi-detail
13) Example of a gravitational wave in an exact theory (sandwich wave)
[Bičák, Rudenko, section 4.2]
... Martin Povišer (04-01)
... may be examined in semi-detail
14) Thermodynamics, hydrodynamics, electrodynamics, geometrical optics, and kinetic theory
[MTW, section 22]
... Camille Landri (04-01)
... should know basic equations in GR setting
References:
Votruba: Základy speciálni 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)
4th January -- Chandrasekhar limit, Sandwich wave in exact theory, Non-gravitational physics within GR
REMARX: