CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Relativistic Physics 2

Code Completion Credits Range Language
02REL2 Z,ZK 6 4+2 Czech
Garant předmětu:
Oldřich Semerák
Lecturer:
Oldřich Semerák
Tutor:
Oldřich Semerák
Supervisor:
Department of Physics
Synopsis:

Lagrangian formalism and conservation laws in general relativity. Initial value problem, 3+1 splitting and Gauss-Codazzi equations. Hamiltonian formalism in general relativity. Causal structure of spacetime. Geometry of timelike and null congruences.

Requirements:

Knowledge of general relativity is presumed on the level of lectures 02OR and 02REL1.

Syllabus of lectures:

1. Lagrangian formalism and conservation laws in general relativity

2. Initial value problem in linear and nonlinear theories

3. 3+1 splitting of spacetime, Gauss-Codazzi equations

4. Hamiltonian formalism in scalar theories, in electromagnetism, and in general relativity

5. Causal structure of spacetime

6. Geometry of timelike and null congruences, Frobenius theorem

Syllabus of tutorials:

1. Gravito-electromagnetism (in linearized theory)

2. Integration in curved spacetimes

3. Gravitational lensing

4. Post-Newtonian expansion, energy-momentum pseudotensors

5. Generation of waves in linearized theory of gravity

6. Gravitational waves in curved spacetime

7. Energy, momentum and angular momentum of gravitational field

8. 3+1 splitting of spacetime

9. Globally hyperbolic spacetimes

10. Asymptotical flatness

11. Gravito-electromagnetism (in exact theory)

Study Objective:

Knowledge:

Learn the description of astrophysical phenomena in terms of general relativity.

Skills:

Solving simple examples from astrophysics.

Study materials:

Key references:

[1] Bičák J., Ruděnko V. N., Teorie relativity a gravitační vlny (skriptum UK, Praha 1986)

Recommended references:

[3] Misner C. W., Thorne K. S., Wheeler J. A.: Gravitation (Freeman, San Francisco 1973)

[4] Weinberg S.: Gravitation and Cosmology (J. Wiley, New York 1972)

Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-08
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