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