I’m studying a PhD in Theoretical Physics (quantum field theory, to be specific), but I would like to learn more about black holes (and related areas. Does anyone have any suggestions for textbooks/available notes on these subjects for people without much background in them? Obviously I’m very comfortable with mathematics and physics in general so I’m not looking for “pop science” material.


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  • $\begingroup$ After a quick skim through Carrol's intro to black holes, check these crisp notes by Townsend wholly on black holes- arxiv.org/abs/gr-qc/9707012. $\endgroup$ – Avantgarde Jun 27 at 22:51
  • $\begingroup$ Also check out John Baez's GR Tutorial. $\endgroup$ – PM 2Ring Jun 27 at 22:57
  • $\begingroup$ Well first of all, do you know any tensor calculus? In order to get to grips with what is happening you will probably want to speak the appropriate language. $\endgroup$ – Rumplestillskin Jun 27 at 23:29

Blackholes are the solution to Einstein's equation. For the introduction, how these solutions/geometries have been obtained look at the textbook

  1. Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll This book is very easy to read and understand. More focus should be on the Penrose diagram (Various coordinate systems) which are very crucial to understand the Blackholes.

Having equipped with general solutions, You can start to learn more about Quantum fields in that spacetime. This will lead to Blackhole information Paradox. This paradox has been resolved up to some extent in AdS/CFT Correspondance. For understanding the quantum nature of Blackhole,


This reference is to understand the information loss problem and How spacetime can be view as quantum entanglement.

  • $\begingroup$ That’s also answered all of the “simplest” questions I had about black holes too! Thanks a lot! :-) $\endgroup$ – CS1994 Jun 27 at 22:31
  • $\begingroup$ @CS1994 If you have anything particular, Then I can add references to those. $\endgroup$ – Hare Jun 27 at 22:33
  • $\begingroup$ @Hare How has AdS/CFT been able to resolve (to whatever extent) the paradox? $\endgroup$ – Avantgarde Jun 27 at 22:51
  • $\begingroup$ @Avantgarde The idea behind it is related to the unitary evolution in CFT. For Small BH, where everything is in the radiation, We can just start from one state in CFT and then evolve it unitarily. But big BH, there is a subtle problem regarding decay of two-point function(information) from the bulk side while this two-point function oscillates from the boundary side. But essentially we know the answer from CFT side. How to reproduce those results from bulk requires quantum gravity correction. $\endgroup$ – Hare Jun 28 at 0:08
  • $\begingroup$ @Hare I understand the heuristic picture, but is there a rigorous proof that CFT evolution implies that the gravity sector is information-loss-free? Also, I suppose gauge-gravity duality has not much to say about astrophysical black holes, which are not in AdS? $\endgroup$ – Avantgarde Jun 28 at 14:39

In addition to Sean Carroll’s Spacetime and Geometry, I will also point out this course on Coursera by Emil Akhmedov. This is a more problem and assignment oriented course.


The most complete but rigorous text on black holes is "The Mathematical Theory of Black Holes" by Chandrasekhar. However, this one is terse and requires knowledge of advanced General Relativity.

Other texts include "A Relativist's Toolkit" by Eric Poisson which discusses the topic and the relevant mathematics in sufficient details and "Gravitation:Foundation and Frontiers" by Thanu Padmanabhan includes discussions on some crucial conceptual ideas on the subject that are usually not found elsewhere.

Apart from Carroll's text (mentioned in other lectures), there are nice lecture notes on the subject like Black Holes from A to Z by Andrew Strominger and Introductory lectures on Black Hole Thermodynamics by Ted Jacobson (if you are interested in the thermodynamics of BHs).


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