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not that im in any way qualified (im a student in aeronautics) but i believe a good textbook in the subject (relativity) should introduce the specific math tools used (as it's been the case with all physics ive encountered).
other than that, a math phd friend of mine has recommended Lee(?)'s introduction to curvature as a textbook on differential geometry. i've actually liked the subject a lot (on the level i had to learn it for my exams), but i was satisfied with the russian textbooks we had.
