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I am currently profficient with basic Einstein index notation, however there are many advanced things with Lorentz indices (such as derivatives, differences between which index is written first on a tensor, ...) that are simply foreign to me since we never really touched on them in class.

I wish to bulletproof my knowledge about Lorentz indices for my GR course and further study, so I am seeking for a realiable, all encompassing document or a book that would cover it.

The book or a document should come with worked examples, so I can do some exercises and realize just how everything works.

I will be glad for all recommendations

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  • $\begingroup$ Any standard textbook on GR will introduce necessary index/ notation conventions. See for instance, chapter 1 from The mathematical theories of Blackholes by S. Chandrasekhar $\endgroup$
    – KP99
    Commented Oct 26, 2022 at 17:58
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    $\begingroup$ Please, check your definition of proficiency, if you think yourself as proficient in Einstein index notation but you have doubts on the order of indices. For a good introduction to vector/tensor algebra and calculus, even if not in the framework of GR, try to have a look here oaktrust.library.tamu.edu/handle/1969.1/2500 $\endgroup$
    – basics
    Commented Oct 26, 2022 at 18:26

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