Black Holes 2005  
Jan 24 Mon 
=15:1517:00 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 
=10:0011:45 room FL72
[=2nd lecture=]
Parallel transport. Covariant derivative. Geodesic lines. Frenet's formulae. 
Jan 31 Mon 
=15:1517:00 room FL64
[=3rd lecture=]
Curvature. Riemann and Ricci tensors and their geometrical meaning. Intrinsic and extrinsic curvature. Examples: sphere, cyllinder. 
Feb 02 Wed 
=10:0011:45 room FL72
[=4th lecture=]
Minkowski spacetime. Spacelike, timelike and null curves. Observers. Measurements. Lorentz transformations. Uniformly accelerated observer. 
Feb 07 Mon 
=15:1517:00 room FL64
[=5th lecture=]
General spacetime. Geodesic deviation. Einstein's principle of equivalence. Gravitational field. 
Feb 09 Wed 
NO LECTURE TODAY

Feb 14 Mon 
=15:1517:00 room FL64
[=6th lecture=]
Matter. Stressenergy tensor. Killing vectors. Conservation laws. 
Feb 16 Wed 
=10:0011:45 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 
=15:1517:00 room FL64
[=8th lecture=]
The effective potential. Epicyclic frequencies. Peryhelion of Mercury advance. 
Feb 23 Wed 
=10:0011:45 room FL72
[=9th lecture=]
Nonstatic spacetimes. The Kerr metric. Ergosphere. Dragging of inertial frames. The Penrose process. 
Feb 28 Mon 
NO LECTURE TODAY

Mar 02 Wed 
=10:0011:45 room FL72
[=10th lecture=]
Conformal transformations. Optical geometry. Centrifugal force paradox. 
Feb 07 Mon 
=15:1517:00 room FL64
[=11th lecture=]
Kruskalization. The horizon. The singularity. Cosmic censorship. The area of horizon theorem. Quantum effects. Hawking radiation. 
Mar 09 Wed 
=10:0011:45 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. 