In our problem session today, we briefly discussed the Hawking effect and how to combine GR and QFT. If you want to learn more about that, take a look here:

http://www.uio.no/studier/emner/matnat/fys/FYS4170/h17/beskjeder/qft-in-curved-spacetime.html

Her er en god innf?ring i tensorregning som kan utdype en del av det vi har jobbet med: 

http://web.mit.edu/edbert/GR/gr1.pdf

Artikkelen har imidlertid noen begrensninger. Den har ikke med Cartans strukturlikninger og likning for komponentene av Riemanns krumningstensor gjelder bare i koordinatbasis. 

Den mest komplette og fineste innf?ringen finnes i Misner, Thorne, Wheeler: Gravitation.

Next Thursday (24th) will be our last problem session and I will use it to wrap up our discussion on black holes and to summarise the key ideas of the lecture. 

There will be a slight change of time: We will start already at 9.30 and the first 45 min will be about black holes. At 10.15 I will start with the repetition part, so you can decide to which part you will want to come. We will finish at 11.30.

Also, if black holes are not enough of a motivation, there will be coffee and cookies. ;)

You will now find a sheet with two additional exercises on black holes that you are invited to look at until next time (24.5.).

There was a mistake in an exercise in the lecture notes. See the correction that was uploaded.

Next week's problem session will be moved to Friday, 4.5. from 14.15 to 15.45. We'll be in seminar room ?394.

The list on important topics that are relevant for the exam was just updated.

Problems for week 17:

Take another look at exercise 6.6. from the textbook ("The tidal force pendulum and the curvature of space") and use the hints given in the problem session.

To round off our discussion about the curvature tensor and flat/curved spacetime, show that the vanishing of the Riemann tensor is a sufficient condition for spacetime to be flat everywhere. Does this imply that spacetime is a globally trivial flat space?

You will now find a sheet with useful formulae that will be attached to the exam problems.

The problem session on Thursday, 19.4.2018, will be moved to Seminarrom ?394 and will start at 12.15. 

In the weekly exercises section, you will now find a set of exercises (and solutions) to practice calculations with differential forms. 

Problems for week 15 from textbook:

6.6. The tidal force pendulum and the curvature of space

Note that our next problem session will start at 10.00!

This is an extra problem for everyone who would like to have some fun with GR during the Easter break. Study geodesic curves on the sphere. Look for example at problem 5 in chapter 3 in Carroll's book.

Happy Easter!

Problems for week 11 from textbook:

5.1. Spatial geodesics in a rotating RF

5.4. Parabolic coordinates

5.5. Covariant derivative

5.6. Geodetic curves in space

Next week's problem session (15.3.) will be in seminar room ?358 as Kristian Birkelands auditorium will be occupied that day. The time stays the same: 10.15-12.00

Problems for week 9 from textbook:

4.2 Free particle in a hyperbolic reference frame

4.3 Uniformly accelerated system of reference

There will be no problem session in week 9 (1.3.2018). Instead, we will have a longer session in week 10.

Problems for week 8 from textbook:

4.1 Relativistic rotating disc

4.2 Free particle in a hyperbolic reference frame

Problems for week 7 from textbook:

3.6 4-Vectors

3.7 Wedge-products of forms 

3.8 Coordinate transformations in a 2-dimensional Euclidean plane

Problems for week 5 from textbook:

1.5 The strength of gravity compared to the Coulomb force

1.6 Falling objects in the gravitational field of the Earth

1.7 A Newtonian black hole

Problems for week 4 from textbook:

1.1 A tidal force pendulum

1.2 Newtonian potentials for spherically symmetric bodies

1.3 The Earth¨CMoon system

1.4 The Roche limit

The discussion group will meet every Thursday in Kristian Birkelands auditorium at 10:15.

The course will be based on the following text book:
?yvind Gr?n: Lecture notes on the General Theory of Relativity. Springer 2009.