Relativistic Physics 2

Course guarantor:

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)

[2] Kuchař K.: Základy obecné teorie relativity (Academia, Praha 1968)

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 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Matematická fyzika (elective course)