Relativistic physics II


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

spring term 2021, 4/2 exam/credit

Short syllabus:

Lagrangian formalism and conservation laws in GR. 3+1 splitting of space-time, Gauss-Codazzi equations. Initial (Cauchy) problem in GR. 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 9:50-12:05 and 13:10-15:25, presently taught in English via the Zoom application.
Invitation: link
Meeting ID: 998 827 6224
Passcode: 369661

Lectures were recorded, videos are linked at the bottom of this page. If you noticed anything we should delete from the recordings, please tell us.
Organization was the same as in previous term, with student talks delivered as web presentations. 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.

Topics of student seminar talks:

  • (also required at exam, but not all in detail -- see the last entry on this page)
  •   1) Generation of waves in the linearized theory of gravitation -- examples [Bičák & Rudenko, section 3.5]
          ... Marek Pospíšil (March 1)
      2) Integration in curved spacetime [Bičák & Rudenko, section 2.5; also useful is section 1.2
          ... Matěj Mezera, Václav Mikeska (March 8)
      3) Energy, momentum and angular momentum of a gravitational field [Bičák & Rudenko, section 2.6; see also MTW, chapter 20]
          ... Richard Škultéty, David Vokrouhlický (March 15)
      4) Gravitational waves on curved backgrounds [Bičák & Rudenko, section 5.3; more details in MTW, chapter 35]
          ... Václav Růžek (March 22)
      5) Waves in the slow-motion approximation [MTW, sections 36.9.-36.11.]
          ... Matúš Papajčík (March 29)
      6) 3+1 decomposition of space-time [Lecture notes, Chapter 24, mainly in detail sections 24.4-24.6]
          ... Matěj Mezera (April 12)
      7) Globally hyperbolic space-times [Joshi, section 4.4]
          ... Dan Rod, Jakub Novotný, Richard Ivánek (April 19)
      8) Asymptotic flatness and lite-cone cuts of infinity [Joshi, section 4.7]
          ... Dan Rod, Jakub Novotný, Richard Ivánek (April 26)
      9) Gravitational lensing [several references on lensing (see presentation)]
          ... Vít König (May 3)
    10) Parameterization of the scalar field in Minkowski spacetime [lecture notes by K. Kuchař]
          ... Pavel Šklíba (May 10)
    11) Gravito-electromagnetism (in linearised theory) [Lecture notes, Section 22.7]
          ... David Spitzkopf (May 17)
    12) Classical and relativistic polytropes [notes from several textbooks (specified in email)]
          ... George Ellis Turner (May 24)
    13) Gravito-electromagnetism (in exact theory) [paper by F. Costa & J. Natário (2014), section 3]
          ... Lukáš Knob (May 31)


    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 recorded files (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

    topics examined