20 questions
for the "Black Hole" course, Chalmers, January - March 2004 Four questions will be asked during the exam. | |
1 | Derive the redshift formula in Minkowski spacetime |
2 | Argue that c^{5}/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 X^{i},
Y^{i} it is
X^{i}D_{i}Y_{k} = - D_{i}(XY)/2, where D_{i} 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 |