Notes updated to 28.04.2023

The notes have been updated to include the last and final lecture. Thanks to all who participated, either live or by going through the videos/notes later on. 

This is not the final version of these notes, when I have a little time I plan to re-organise them a little bit to make a smoother logical flow. Whenever that happens, the notes will be uploaded to the shared folder and I'll mention it on this blog page.

Finally, thanks to Rajesh Gopakumar for his encouragement and ICTS for constant support that made this series happen. I particularly thank the AV staff and administrative staff for handling the practical issues, and Aditya Sharma and Omkar Shetye for coordination.

In future, comments/questions can still be posted on this blog, they reach my mailbox and I will try my best to respond. 

Notes updated to 24.04.2023

  The lecture notes have been updated to 24.04.2023 and are available in the shared folder.

Notes updated to 21.04.2023

 The notes are now updated. I have put in a detailed explanation of why the Schwarzschild solution leads to trapped surfaces inside the horizon.

Notes updated to 17.04.2023

 The lecture notes have been updated to 17.04.2023 and are available in the shared folder.

Notes updated to 15.04.2023

 The course notes have been updated to 15.04.2023 in the shared folder.

Updated list of topics for the course

Like all such lecture courses, one either has to extend the number of lectures or modify the ambitious initial plan of what will be covered! Unfortunately I cannot extend this course beyond 12 lectures due to other commitments. 

Therefore, a revised plan for this course is as follows.

List of topics:

1. Brief review of basic General Relativity and relevant mathematics. [1]

2. Geometry and topology of spacetimes: causality, Cauchy hypersurfaces, globally hyperbolic space-times. [3]

3. Geodesics, focusing and Raychaudhuri equation. [2]

4. Hawking and Penrose singularity theorems. [3]

5. Black holes: brief review, causality properties, cosmic censorship, area theorem [2]

6. Origins of black hole thermodynamics. [1]

Total: 12 lectures of 90 minutes each. [ ] = number of lectures assigned to each topic. 

If there is interest, later in 2023 I could give another set of lectures on Black Hole Thermodynamics including recent developments.

Notes updated to 10.04.2023

The updated notes have been placed in the shared folder.

Change in date of this Friday lecture

 The lecture originally scheduled for Friday April 14 at 4 PM IST has been shifted to Saturday April 15 at 4 PM IST. Only for this week!

Notes updated to 7.4.2023

 The updated notes have been placed in the shared folder.

Please note there is a strong chance that the lecture on 14.4.2023 will be re-scheduled due to some special activity at ICTS. The date and time of the replacement lecture will be posted here as soon as it is decided.

Notes updated to 03.04.2023

The notes have been updated to 03.04.2023. Also I have included figures for the previous lecture, which I had missed out in the last update.

Notes updated to 30.03.2023

The notes, updated to include my lecture on 30.03.2023, have now been uploaded to the shared folder. I apologise for the delay.

There is a small change in the notes compared to the lecture. I realised that the entire compactness proof for the space of curves from P to Q can be stated in terms of sequential compactness, which involves convergence of sequences and convergence curves, without separately mentioning limit points or limit-point compactness. So I have re-stated everything in terms of sequential compactness. This makes it a little shorter, and I hope also clearer.

As I mentioned once before, I often make changes to earlier parts of the notes as well, and indeed I added a few points here and there -- including the references that I'm using so far. So you may find it useful to go through the notes from the beginning. I also have a plan to make the figures a little more elegant using some software, but as of now I can't guarantee this will happen.