Relativistic physics II

NTMF038

prof. RNDr. Jiří Bičák, DrSc., dr.h.c., doc. RNDr. Oldřich Semerák, DSc.

spring term 2022, 4/2 exam/credit

Short syllabus:

Lagrangian formalism and conservation laws in field theories and in GR. Initial (Cauchy) problem in linear and non-linear theories, specific nature of the initial-value problem in GR. 3+1 splitting of space-time, Gauss-Codazzi equations. Hamiltonian formalism in scalar-field theory, in electrodynamics and in GR. Concepts of causal structure (different "levels of predictability"). Geometry of time-like and null congruences, Frobenius theorem. Relativistic strings.

A follow-up of the course NTMF037 – Relativistic physics I (in fall term).
Mainly suitable as a master course for theoretical physicists.

Time, space, rules:

Monday from 13:10 to about 17:50, presently taught in English.

Organization is the same as in previous term, with student talks typically delivered later in the afternoon. 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.
Examination in Czech as well as in English may be chosen. In preparation for the exam, lecture notes may be used freely. Links to videos from the 2020/21 run may be helpful -- see below.

Student seminar talks (some of them just offered):

(also possibly discussed at exam, but not in detail, "just idea")

1) Thermodynamics, hydrodynamics, electrodynamics, geometrical optics, and kinetic theory [MTW, section 22]
      ... Poula Tadros Nashed (February 26)
2) Gravito-electromagnetism (in linearised theory) [Lecture notes, Section 22.7]
      ... Tomáš Hale, Viktor Vařeka (March 4)
3) Integration in curved spacetime [Bičák & Rudenko, section 2.5; also useful is section 1.2
      ... Tomáš Moravčík (March 11)
4) Gravitational lensing [papers by Wambsganss (LRR 1998) and by Bartelmann (CQG 2010); "story" in Lecture notes 17.1.5]
      ... Radka Křížová, Michal Krtouš (March 18)
5) Post-Newtonian expansion, usage of energy-momentum pseudotensors
      ... Álvaro Rafael Martínez Gómez (March 25)
n) Generation of waves in the linearized theory of gravitation -- examples [Bičák & Rudenko, section 3.5]
      ... ??? (???)
n) Gravitational waves on curved backgrounds [Bičák & Rudenko, section 5.3; more details in MTW, chapter 35]
      ... ??? (???)
n) Energy, momentum and angular momentum of a gravitational field [Bičák & Rudenko, section 2.6; see also MTW, chapter 20]
      ... ??? (???)
n) 3+1 decomposition of space-time [Lecture notes, Chapter 24, mainly sections 24.4-24.6 in detail]
      ... ??? (???)
n) Globally hyperbolic space-times [Joshi, section 4.4]
      ... ??? (???)
n) Waves in the slow-motion approximation [MTW, sections 36.9.-36.11.]
      ... ??? (???)
n) Asymptotic flatness and light-cone cuts of infinity [Joshi, section 4.7]
      ... ??? (???)
n) Gravito-electromagnetism (in exact theory) [paper by F. Costa & J. Natário (2014), section 3]
      ... ??? (???)
n) Parameterization of the scalar field in Minkowski spacetime [lecture notes by K. Kuchař]
      ... ??? (???)
n) Classical and relativistic polytropes [notes from several textbooks (specified in email)]
      ... ??? (???)

References:

Bičák, Rudenko: Teorie relativity a gravitační vlny (skripta)
Misner, Thorne & Wheeler: Gravitation (can provide good pdf; or you can google it yourselves)
Joshi: Global Aspects in Gravitation and Cosmology
Lecture notes: Relativistic physics