General Theory of Relativity

Scope of questions for State exams of Master's degree program

Branch: Nuclear and Particle Physics

Subject: General Theory of Relativity

Subjects regarding the questions:

02GTR General Theory of Relativity

1. Einstein equivalence principle

inertial mass and gravitational mass; experiments comparing these masses; formulation of the equivalence principle; locally inertial frames

2. Curved spaces in more dimensions

Riemann spaces; metrics; covariant derivative; Christoffel symbols; tensors; geodesics

3. Einstein equations

Riemann curvature tensor; energy-momentum tensor; Einstein equation

4. Schwarzschild geometry

derivation of Schwarzschild metrics; Birkhoff theorem; geodesics on Schwarzschild metrics; photon trajectory

5. Experimental tests of general relativity
gravitational red shift; precession of Mercury; gravitational light bending; gravitational lenses

6. Black holes

event horizon; gravitational collapse; tidal effects; Kruskal coordinates and Kruskal diagrams

7. Kerr geometry
Kerr metrics; structure of Kerr black hole; dragging of inertial frames

8. .Gravitational waves
Einstein equations for weak fields; gauge transformations; gravitational waves in vakuum; sources of gravitational waves

9. Friedmann-Robertson-Walker geometry
cosmological principle; Friedmann-Robertson-Walker metrics; geodesics in FRW metrics; cosmological red shift; Hubble parameters

10. Cosmological models
components of cosmological fluid; cosmological parameters; evolution of scale parameter; analytical cosmological models