Relativistic physics II


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. Geometry of time-like and null congruences, Frobenius theorem. 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"). 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 ( 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) Energy-momentum pseudotensors
          ... Álvaro Rafael Martínez Gómez (March 25)
      6) 3+1 decomposition of space-time [Lecture notes, Chapter 24, mainly sections 24.4-24.6 in detail]
          ... Tatiana Vargicová (April 8)
      7) Waves in the slow-motion approximation [MTW, sections 36.9.-36.11.]
          ... Jindřich Šándor (April 8)
      8) Generation of waves in the linearized theory of gravitation -- examples [Bičák & Rudenko, section 3.5]
          ... Jan Feireisl (April 15)
      9) Post-Minkowskian approximation (Landau-Lifshitz approach)
          ... Álvaro Rafael Martínez Gómez (April 22)
    10) Causality, globally hyperbolic space-times [Joshi, section 4.4]
          ... Viktor Vařeka (April 29)
    11) Energy, momentum and angular momentum of a gravitational field [Bičák & Rudenko, section 2.6; see also MTW, chapter 20]
          ... Jakub Tyle, Filip Nicek (May 13)
    12) Asymptotic flatness and light-cone cuts of infinity [Joshi, section 4.7]
          ... Vojtěch Doleček (May 20)
      n) Gravitational waves on curved backgrounds [Bičák & Rudenko, section 5.3; more details in MTW, chapter 35]
          ... ??? (???)
      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)]
          ... ??? (???)


    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

    Links to recordings of 2020/21 run by Jiří Bičák (mp4):

    1st March lecture   (notes),      1st March afternoon talk

    8th March lecture   (notes 1,   notes 2),      8th March afternoon talk

    15th March lecture   (notes),      15th March afternoon talk

    22nd March lecture   (notes 1,   notes 2),      22nd March afternoon talk

    29th March lecture   (notes),      29th March afternoon talk

    12th April lecture   (notes,   remark),      12th April afternoon talk

    19th April lecture   and   add for next week   (notes,   correction,   and add for next week),      19th April afternoon talk

    26th April lecture   (notes),      26th April afternoon talk

    3rd May lecture,      3rd May afternoon talk

    10th May lecture   (notes),      10th May afternoon talk

    17th May lecture   (notes),      17th May afternoon talk

    24th May lecture,      24th May afternoon talk

    31st May lecture   (notes),      31st May afternoon talk

    additional resources:
    ADM-energyPalette gravitomagnetiqueEinstein in PragueEinstein and Materialism>,  strings2-addition