Black Holes 2005

Jan 24 Mon =15:15-17:00 room FL64   [=1st lecture=]
Infinitesimal distances on a plane and on a sphere. The meric. Coordinate transformations. Covariant and contravariant vectors and tensors. Tensor algebra. Rasing and lowering indicies. Einstein's summation convention.
Jan 26 Wed =10:00-11:45 room FL72   [=2nd lecture=]
Parallel transport. Covariant derivative. Geodesic lines. Frenet's formulae.

Jan 31 Mon =15:15-17:00 room FL64   [=3rd lecture=]
Curvature. Riemann and Ricci tensors and their geometrical meaning. Intrinsic and extrinsic curvature. Examples: sphere, cyllinder.
Feb 02 Wed =10:00-11:45 room FL72   [=4th lecture=]
Minkowski spacetime. Spacelike, timelike and null curves. Observers. Measurements. Lorentz transformations. Uniformly accelerated observer.

Feb 07 Mon =15:15-17:00 room FL64   [=5th lecture=]
General spacetime. Geodesic deviation. Einstein's principle of equivalence. Gravitational field.

Feb 14 Mon =15:15-17:00 room FL64   [=6th lecture=]
Matter. Stress-energy tensor. Killing vectors. Conservation laws.
Feb 16 Wed =10:00-11:45 room FL72   [=7th lecture=]
Einstein's field equations. Schwarzschild equations. The Schwarzschild metric. Circular motion of particles and photons in the Schwarzschild metric.

Feb 21 Mon =15:15-17:00 room FL64   [=8th lecture=]
The effective potential. Epicyclic frequencies. Peryhelion of Mercury advance.
Feb 23 Wed =10:00-11:45 room FL72   [=9th lecture=]
Non-static spacetimes. The Kerr metric. Ergosphere. Dragging of inertial frames. The Penrose process.

Mar 02 Wed =10:00-11:45 room FL72   [=10th lecture=]
Conformal transformations. Optical geometry. Centrifugal force paradox.

Feb 07 Mon =15:15-17:00 room FL64   [=11th lecture=]
Kruskalization. The horizon. The singularity. Cosmic censorship. The area of horizon theorem. Quantum effects. Hawking radiation.
Mar 09 Wed =10:00-11:45 room FL72   [=12th lecture=]
Astrophysical black holes. Other compact objects: neutron stars and white dwarfs. Stellar mass black holes. Supermassive black holes. Primodial black holes. Black hole in our Galaxy centre.