Relativistic physics II

NTMF038

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

spring term 2026, 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:

Mondays and Wednesday from 13:10 to 15:25 in the ÚTF seminar room on the 10th floor in Troja, presently taught in Czech.

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")

Parallel transport (derived in a different way than in the first semester)
- Resources: [Kuchař, section II.4]
- Presenting:
- Exam requirements: examined, but not in full detail
Equivalent criteria for space-time flatness
- Resources: [Kuchař, section II.6]
- Presenting:
- Exam requirements: examined almost in detail (tricks in computation of "the integral" are not compulsory)
Electro-geodesics in the Kerr-Newman space-time, Carter equations
- Resources: [GTR, section 17.3]
- Presenting:
- Exam requirements: examined in semi-detail (need not learn the metric by heart)
Pericentre shift, light bending
- Resources: [GTR, section 17.1; or also Dvořák]
- Presenting:
- Exam requirements: examined almost in detail (final tricks are not compulsory)
Uniqueness of the Riemann tensor
- Resources: [Kuchař, section II.5.8]
- Presenting:
- Exam requirements: understanding required, without details (transformations)
Angular momentum (spin) and Fermi-Walker transport
- Resources: [Bičák, Rudenko, sections 1.5, 1.6, 2.2; also GTR, chapter 18 (up to 18.1)]
- Presenting:
- Exam requirements: properties of the FW transport in detail, spin-behaviour derivation is not compulsory
Composition of Lorentz transformations, boosts and Thomas precession
- Resources: [Votruba, sections IV.7 and IV.8; also GTR, section 18.2]
- Presenting:
- Exam requirements: you should know "in principle", examined without details
Wave-fronts in field theories
- Resources: [GTR, section 23.1; also Bičák, Rudenko, section 4.1]
- Presenting:
- Exam requirements: may be examined in semi-detail
Linearized theory of gravitation
- Resources: [GTR, sections 22.1-22.4, or Bičák, Rudenko, section 3.1]
- Presenting:
- Exam requirements: examined in detail
Plane waves in the linearized gravity
- Resources: [GTR, sections 22.5 and 22.6, or Bičák, Rudenko, sections 3.3 and 3.4]
- Presenting:
- Exam requirements: examined in detail
Asymptotic form of the field of an isolated source
- Resources: [Bičák, Rudenko, section 3.2]
- Presenting:
- Exam requirements: should just know what it is about
Example of a gravitational wave in an exact theory (sandwich wave)
- Resources: [GTR, sections 23.2 and 23.3; also Bičák, Rudenko, section 4.2]
- Presenting:
- Exam requirements: may be examined in semi-detail
(possibly) Thermodynamics, hydrodynamics, electrodynamics, geometrical optics, and kinetic theory
- Resources: [MTW, section 22]
- Presenting:
- Exam requirements: should know basic equations in GR setting

References:

Bičák, Rudenko: Teorie relativity a gravitační vlny (skripta) (scanned DJVU)
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