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In reference to my question here: What would be essential math topics to read for general relativity (from a particular book)?

I'm reading a book and wanted to get a clear understanding on what topics from that book are essential as mathematical prerequisites for grad level general relativity. I searched before posting as is required, and found no other questions in the same spirit.

Either the answers therein are general book recommendations, e.g. here, or they give a broader idea about what math fields are involved (like "understanding of differential geometry", "abstract algebra topics like scalar product spaces", etc.) - see here. What I'm looking for is much more specific.

I was told that the question is a duplicate (I'm not convinced that it is) and later on that it's opinion-based - again, I'm not so sure because mathematical topics needed to tackle grad level GR doesn't sound like a subjective topic.

I'm hoping that members of the community experienced in GR could help out in that regard, and so it's important for me to have that question open. Could I get some feedback on how I can improve it?

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  • $\begingroup$ Somewhat related: Give each site a parallel site for polling, recommendations and subjective-ish stuff. See also the "Linked" questions on the right on that page. $\endgroup$
    – Peter Mortensen
    Feb 21, 2022 at 15:11
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    $\begingroup$ @PeterMortensen : I don't see how that answers my question. The linked question just suggests whether a different site should be created and a bunch of people are giving their opinions on it. There is nothing concrete there. With all due respect, it'd be helpful to get a specific reason on why my question was closed and how I can improve it. $\endgroup$
    – Shirish Kulhari
    Feb 24, 2022 at 10:58
  • $\begingroup$ Anybody? Can any of the moderators or reviewers of that question let me know how exactly my question was "opinion-based"? $\endgroup$
    – Shirish Kulhari
    Feb 26, 2022 at 12:52
  • $\begingroup$ I don't think @PeterMortensen intended on answering the question with his comment, given that it starts with "Somewhat related". $\endgroup$
    – Kyle Kanos
    Feb 26, 2022 at 17:26

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The tag info tab says,

Questions asking "What is a good book about X?" or more generally, "What should I read to learn about X?", typically where there is not a single authoritative reference. These sorts of questions have multiple answers and will acquire new answers as more books/papers are written on the subject.

and then links to the resource recommendations FAQ wherein you'll see that questions under this tag should be specific about the actual request (material covered, style, etc).

Your question, rather than being of the form "what books should I use to learn GR" (i.e., a resource recommendation) is instead "what chapters of this specific book can I skip?". This type of question is asking for an opinion, as some people might feel all chapters are necessary to learn the material, while others might say you would be able to skip some chapters and still others might say you could skip even more chapters and still consider the material as learned. Ergo, any answer to your question is an opinion and not an objective one that is preferred here.

That said, even adjusting the question to follow the resource recommendation format (which would not be subjective), would be a duplicate of the linked duplicate (Where do I begin in order to study relativity? itself a dupe of Introduction to relativity books and maybe also of Books for general relativity).

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  • $\begingroup$ Thanks for the feedback! Based on what you're saying, GR is too broad a field, so "math to learn GR" will be different to different people. Is that right? In that case, if I'm much more specific in my question about what topics in GR I intend to study (e.g. "math to learn computations involving different kinds of black holes"), will that be okay and non-subjective? $\endgroup$
    – Shirish Kulhari
    Feb 26, 2022 at 18:46
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    $\begingroup$ @ShirishKulhari the issue is that different people working in GR will have different opinions. For example, Weinberg's book avoids talking too much about differential geometry, while Wald's embraces geometry completely. Two different physicists with profound understandings of GR that believe different mathematical prerequisites are essential. The problem is not that GR is too broad, the problem is that "what is essential?" depends on who you are asking $\endgroup$
    – Níckolas Alves
    Feb 26, 2022 at 19:20
  • $\begingroup$ @ShirishKulhari If your interest in GR is for BHs, then you may want to peruse the search [resource-recommendations] is:q black holes', as what you're looking for may have been asked already. $\endgroup$
    – Kyle Kanos
    Feb 26, 2022 at 19:56
  • $\begingroup$ @NíckolasAlves: Thank you so much for explaining and now I understand. I didn't know such vastly different treatments of GR exist and people study it in such different ways. I will try to navigate prerequisites on my own, in that case. $\endgroup$
    – Shirish Kulhari
    Feb 26, 2022 at 21:02
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One big problem I see with this question is that it's very narrow. Part of the philosophy of Stack Exchange is that it should act as a compendium of questions and answers with broad interest. The questions here should be questions that people other than the original poster have or will have in the future. Such people can then find their question already asked and answered here for as long as SE stays around.

Your question seems to be basically "Which sections of this specific book are necessary for learning general relativity?" This is not a question with broad interest for people learning or thinking about physics; it really only applies to people reading that specific book with the goal of applying its contents to GR. I am not sure that your question would not be closed anyway if you tried to make it more broadly applicable, but I think it would be much more likely to stay open if it were about more than one specific book.

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  • $\begingroup$ Thanks for the feedback! Point taken, but the question was closed as "subjective / opinion-based". If I were given the feedback that I should broaden the scope a bit, then I would've edited the question accordingly. Unfortunately what has happened is that the question was closed as opinion-based, and none of the moderators or reviewers of the question have left any feedback or reason as to how it can be considered subjective. $\endgroup$
    – Shirish Kulhari
    Feb 26, 2022 at 12:51
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Read Einstein's 1916 review article on general relativity:

https://einsteinpapers.press.princeton.edu/vol6-trans/158

It starts with the mathematical prerequisites about tensors that you'll need.

There's nothing more enterprising than learning from the master himself! From my personal experience, I had tried learning the subject using several books, but most of them had proved too thick or thin or overwhelming for me.

As a companion book, I found first few chapters of Tensor Calculus by Synge and Schild a fairly useful read:

https://books.google.co.in/books?id=7ey7AQAAQBAJ

Good luck!

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  • $\begingroup$ Alright - I just figured your question's scope is limited to that book you're already reading. Perhaps consider that you might want to recognize that the aforementioned Einstein's article is quite self-sufficient in meeting your learning objective. $\endgroup$
    – John Doe
    Feb 25, 2022 at 1:07
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    $\begingroup$ This doesn't answer the question asked, which is about improving the question they'd asked on the main site. $\endgroup$
    – Kyle Kanos
    Feb 26, 2022 at 17:27
  • $\begingroup$ @JohnDoe: Hi, thanks! I will check out the book that you linked to. As far as I know though, the modern formalism wasn't much fleshed out when Einstein wrote his original papers, so that might be an issue. $\endgroup$
    – Shirish Kulhari
    Feb 26, 2022 at 18:53

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