Reading course on "Basics of black holes and black holes in string theory"
Email: harmark at nbi.dk
This is a reading course intended for people who already know a little about black holes, for example from Poul Olesens General Relativity course, but would like to learn more. The main part of the course is about basic results on black holes in 4 dimensions, such as a mathematical description of event horizons and the thermodynamics of black holes. Later in the course there will also be something about black holes in string theory and M-theory, specifically their generalizations as charged black branes. Finally, if time permits, there will be something on black holes in five dimensions which most of the modern string-theory inspired black hole research is focused on at the moment.
Black holes is today at the center stage in the theoretical high-energy research. One of the main problems in unifying quantum mechanics and General Relativity is how to explain the quantum nature of a black hole. In string theory black holes plays a central role in the understanding of non-perturbative effects. Specifically in the AdS/CFT correspondence it is possible to relate black hole physics to physics of gauge theories.
The reading course is largely a self-study course. Each student (master or phd) can either get ECTS credit for the course, or it can count for their "hovedfagskollokvium". There will be given 7.5 ECTS for active attendence to the course and a two hour presentation of part of the subject. If the student instead chooses to use it for the "hovedfagskollokvium" then the two hour presentation will count for the "hovedfagskollokvium".
If you are interested in participating in this course, please send me an email.
We meet Friday Nov. 7 at 11:00 in Aud. B (Blegdamsvej 17) to organize the course, including who should speak when.
Duration: 2008: Week 46,47,48,49,50,51; 2009: Week 2,3,4
Room: MA-14 (Blegdamsvej 21)
Time: Thursday 13:15 to 15:00
People attending the course and giving one of the lectures (and getting credit for the course):
Ask Emil Jensen
Martin Cramer Pedersen
Lea Hildebrandt Rossander
Mads Toudal Frandsen
People attending without giving a lecture (and without getting credit):
Andreas Vigand Pedersen
Postdocs and senior people:
Notes on Killing vector fields and other geometric stuff. Download it here
“Black holes”, Lecture notes by Paul K. Townsend, arXiv:gr-qc/9707012. Download it here
Notes on causality and the global definitions of the event horizon. Download it here
Notes on physical quantities, black hole mechanics and thermodynamics. Download it here
“Lecture Notes on General Relativity” by Sean M. Carroll, arXiv:gr-qc/9712019 (Chapter 7, pages 164 – 216) . Download it here
“Gravity and strings” by Ortin
My paper arXiv:hep-th/0408141. Download it here
Other material: Nice project on black hole physics written by Andreas Vigand Pedersen. Download it here
Schedule for lectures:
Lecture 1, 13/11: Martin Krrsak
Lecture 2, 20/11: Ask Emil Jensen
Lecture 3, 26/11: Martin Cramer Pedersen
Lecture 4, 4/12: Joakim Sandroos
Lecture 5, 11/12: Esben Mølgaard
Lecture 6, 18/12: Lea Hildebrandt Rossander
Lecture 7, 8/1: Mads Toudal Frandsen
Lecture 8, 15/1: Jay Armas
Lecture 9, 22/1: Pawel Caputa
Killing vector fields, stationary and axisymmetric space-times
Null hypersurfaces, Killing horizons and surface gravity
Global characteristics of a space-time and Carter-Penrose diagrams (sec. 2.4 of Townsend, see also Chapter 7 in Carroll)
Lecture 4: Global definition of the Event Horizon (my notes on causality and the global definitions of the event horizon, plus sec. 2.6 and 2.7 of Townsend).
Lecture 5: The black hole Uniqueness theorems and properties of rotating black holes (Chapter 4 of Townsend)
Lecture 6: Measurement of physical quantities, black hole mechanics and the Penrose process
Lecture 7: Hawking radiation
Lecture 8: Black branes in higher dimensions as generalizations of black holes in four dimensions (Chapter 18 in Ortins book).
Lecture 9: Five-dimensional asymptotically flat black holes (Literature: arXiv:0801.3471 and hep-th/0408141)