Exercise Class Log
Log for lectures (Teresia)
[C]=Ta-Pei Cheng, Relativity, Gravitation and Cosmology, Oxford 2010.
[D]=Lecture notes by P. Dunsby
Lecture1: Gave a short overview of the topic. Said some basic things about Galilean transformation and Lorentz tranformation. It is good to read several different description of this topic, then it is easier to understand. Eg besides the book test Dunsby or Wikipedia. Next time I will go through the index notation in detail and tell some basic things about tensors. So don't miss that! They don't bite!
Lecture2: Talked about index notation and a short repetion of the ch. curvilinear coordinates in the vector analysis course. Talked about contravariant and covariant vectors and tensors. Important 4-vectors. Started talking about Space-time diagram. Here is a fun page on internet on that: Space-time diagrams
Lecture3: Finally did the barn paradox! Talked more about space-time diagram. Talked about the modern view of tensors following Carroll's notes. Started discuss electromagnetism in its tensor formalism. Will show next time the beauty with it.
Lecture4: Talked about electromagnetism in its tensor formalism. The energy momentum tensor. Said some comments on the twin paradox.
Lecture5: Talked about the weak and strong Equivalent Principle. A bit historical perspective. Mainly a motivation for Einsteins geometrical theory of gravity. Promised to do an experiment next time.
Lecture6: Didn't do the experiment, have to find a small heavy thing first.
Did curved spaces. Reviewed a bit from working with curvilinear coordinates in flat space. Then introduced covariant derivative, parallel transport and geodesics. Two different equivalent ways of define the geodesic. Mentioned the subtle thing with the statement that you can square the length and get the same equation. Will talk more about it next time.
Lecture7: Talked alot about curvature. First about the curvature of a one-dimensional curve. You can find some information here: Curvature. This leads to an alternative definition of Gaussian curvature: Curvature Curvature
Lecture8: Introduced a curved space time to describe gravity. Showed that the newtonian limit of the geodesic equation leads to Newton's EOM for gravity. Then I talked a bit about gravitational redshift from the point of view of curved geometry. Tidal force. In the end I said something briefly about the Schwarzschild metric. Showed a special lens which has a cool effect of bending light in the same way as planets and stars, such that you see that the light from a point source become a circle.
Lecture9: Talked about geodets in the Schwarzschild geometry. How general relativity corrects the Mercury orbit. Look here also: Kepler
Lecture10: Repition about tensors and summary. Curvature in general dimensions. In the End Einsteins equation.
Lecture11: More about Einsteins equation. Took the Newtonian limit to check the consistency and to fix the constant "kappa". The Schwarzschild solution, scetchy. Start discuss a bit cosmological solutions to EE.
Lecture12: Talked a bit about the cosmological constant. Then talked about the simplest black hole, in different coordinate systems. To see that the horizon is just a coordinate singularity in Schwarzschild coordinates.
Lecture13: Continue talking about black holes. First about orbits around black holes and then continue talking about rotating black holes which has some more complicated structure and interesting features. Forgot to say that in the ergodetic region particles with negative mass can be created and then leave, thus a good power station. The black hole bomb I forgot to mention also...
Second half I gave a introduction to cosmology. Brief history of the Universe. The Hubble's measurement leading to the Hubble law and it consistency with the Robertsson-Walker metric. Also mentioned the critical density, the measurement and its relation with dark materia and dark energy.
Lecture14: Talked about the time evolution of the Universe depending on density and curvature. Then talked about the flatness problem and horizon problem and how they can be solved with the inflation model. I also said something about how to use CMB measurement to conclude that our universe is almost flat. Here is a nice review Cosmology