Relativistic Physics I

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

Tensor analysis. Schwarzschild solution of Einstein equations. Black holes and gravitational collapse. Relativistic theory of stellar equilibria and evolution. Linearized theory and gravitational waves.

Requirements:

Knowledge of general relativity is presumed on the level of 02OR lecture.

Syllabus of lectures:

1. Tensor analysis - tensor densities, covariant divergence, Fermi-Walker transport

2. Schwarzschild's solution of Einstein equations - properties, analytical extension, pericenter precession and light bending

3. Solutions of Einstein equations describing stationary black holes - Reissner-Nordström, Kerr and Kerr-Newman metric

4. Gravitational collapse and blackholes - uniqueness theorems, blackhole formation, blackhole thermodynamics, energy extraction

5. Theory of stellar equilibrium and evolution - radial oscillations and stability of spherically symmetric stars

6. Final stages of stellar evolution - white dwarfs and neutron stars, Chandrasekhar limit

7. Linearized theory and plane gravitational waves

Syllabus of tutorials:

1. Composition of Lorentz transformations - Thomas precession

2. Parallel transport

3. Angular momentum and Fermi-Walker transport

4. Uniqueness of Riemann tensor

5. Criteria of spacetime flatness

6. Petricenter precession, light bending

7. Electro-geodesics in Kerr-Newman metric

8. Linearized theory of gravity

9. Gravitational plane waves in linearized theory

10. Asymptotic form of field of isolated source

11. Exact gravitational wave

Study Objective:

Knowledge:

Get advanced knowledge of general relativity including basic solutions of Einstein's equations.

Skills:

Solving advanced examples in general relativity.

Study materials:

Key references:

[1] Bičák J., Ruděnko V. N.: Relativity Theory and Gravitational Waves (in Czech), UK, Praha 1986

[2] Kuchař K.: Foundations of General Relativity Theory (in Czech), 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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematická fyzika (elective course)