GIAN course on the black hole information paradox

On behalf of the organizers and the faculty participating in the programme, welcome to the GIAN course on the black hole information paradox.

This is expected to be an intensive 2-week course, with lectures, tutorials and discussions. The information paradox, first found by Hawking in 1975, is perhaps the most important issue in fundamental theoretical physics today. The goal of the course is to make the students well versed in this problem, so that they can work in this area, or use its insights in other related areas of physics.

With this goal in mind, it is best if the students work through preparatory material on the problem before they arrive at the course. I will be posting some lecture notes on this website. You are strongly encouraged to work through these notes. I would also encourage you to make a Latex file for yourself, where you type in questions that you have, as well as computations that you perform when preparing for the course. This file will help you in the discussions sections where you will be asked to bring questions/issues to the whole class.

The notes below are incomplete in many ways (since I am in the process of writing them): there are many typos, and some sections are yet to be filled in. But they should be useful to work through nevertheless as a supplement to the lectures.

If you have questions/comments for me before the course you can email me at

Lecture notes 1: Introduction to the paradox

Lecture notes 2: Overview of general relativity

Lecture notes 3: Overview of field theory, derivation of Hawking radiation

Lecture notes 4: The no-hair theorem

Lecture notes 5: An overview of string theory

Lecture notes 6: Finding the entropy of black holes in string theory

Lecture notes 7: Resolving the paradox: the fuzzball construction

Lecture notes 8: The idea of AdS/CFT duality

Lecture notes 9: The small corrections theorem

Lecture notes 10: The breakdown of the semiclassical approximation at the horizon

Lecture notes 11: Infall into black holes: the idea of fuzzball complementarity

Lecture notes 12: The idea of wormholes, and its difficulties

Lecture notes 13: Alternative proposals for resolving the information paradox

Lecture notes 14: The questions in cosmology

Lecture notes 15: Appendices