20 questions for the "Black Hole" course,
Chalmers, January - March 2005

Four questions will be asked during the exam.
1 Derive the redshift formula in Minkowski spacetime
2 Argue that c5/G is the upper limit for power
3 Show that from the Killing equation follows that there exist a coordinate system in which the metric tensor does not depend on one particular coordinate.
4 Show that for the two commuting Killing vectors Xi, Yi it is
XiDiYk = - Di(XY)/2,
where Di denotes covariant derivative, and () scalar product.
5 Show that Schwarzschild's spacetime is conformally flat. Discuss physical meaning of conformal coordinates
5 Discuss the optical geometry for Schwarzchshild space.
5 Discuss the embedding technique.
6 Discuss circular motion of particles in Schwarzschild's spacetime using the effective potential method.
7 Calculate radius and Kepler's frequency for the marginally stable orbit in Schwarzschild's spacetime
8 Calculate radius and Kepler's frequency for the marginally bound orbit in Schwarzschild's spacetime
9 Calculate radius and Kepler's frequency for the photon orbit in Schwarzschild's spacetime
10 Calculate the epicyclic frequency in a nearly circular motion in Schwarzschild spacetime
11 Calculate acceleration of a static observer in Schwarzschild's spacetime
12 Discuss radial motion of particles and photons in Schwarzschild's spacetime
13 Estimate Hawking's temperature using dimensional arguments. Calculate the temperature for ten solar mass black hole and discuss astrophysical consequences of the calculated value.
17 Derive formulae for conserved quantities in perfect fluid motion in Scwarzschild's spacetime
18 Discuss the efficiency of black hole accretion
19 Discuss types of astrophysical black holes
20 Estimate the minimal mass of a primodial black hole using dimensional arguments