Reading course on "Basics of black holes and black holes in string theory"


Troels Harmark

Email: harmark at

Office: FC4




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.


Practical stuff:


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):


Master students:

Ask Emil Jensen

Martin Krssak

Esben Mølgaard

Martin Cramer Pedersen

Lea Hildebrandt Rossander

Joakim Sandroos


PHD students:

Jay Armas

Pawel Caputa

Mads Toudal Frandsen


People attending without giving a lecture (and without getting credit):



Laura Gava

Johan Samsing

Andreas Vigand Pedersen


Postdocs and senior people:

Niels Obers

Marta Orselli




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


Course plan:


Lecture 1:

Killing vector fields, stationary and axisymmetric space-times


Lecture 2:

Null hypersurfaces, Killing horizons and surface gravity


Lecture 3:

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)