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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 |