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I Are many exercises in Schutz just too hard?

  1. Oct 4, 2016 #1
    Dear all,
    I am self-studying GR using A First Course in General Relativity by Bernard F Schutz. I am halfway through the course, trying to solve all the exercises. But I worry that I can solve maybe 80% of them, the remaining 20% I find them just too hard.
    I know I am no genius, and I don't have anyone to compare against. I would like to hear from people who have walked this path before.
    Sometimes, the exercises seem to expand on topics that aren't covered in the text rather than being real exercises that the student is supposed to solve on their own.
    As an example, without having mentioned Killing fields before in the text, an exercise defines the Killing equation as $$\nabla_\alpha \xi_\beta + \nabla_\beta \xi_\alpha = 0$$ and asks to prove that along a geodesic, ##p^\alpha \xi_\alpha## is constant.
    I couldn't do this one. I am not asking for a proof, because I already found it elsewhere and I thought it very instructive. My question is rather whether most students can be expected to solve this exercise. If so, maybe I should work harder on my tensor algebra proficiency before going any further.
    Thank you
    Last edited: Oct 4, 2016
  2. jcsd
  3. Oct 7, 2016 #2

    Simon Bridge

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    What does "just too hard" mean?
    Everybody will struggle with some of the exercises - different students struggle with different ones according to their prior experience, skills, effort and talents.
    Are you studying this by yourself?
    The text is really intended to accompany a lecture course with other study material, assignments, tutors, and other students.
  4. Oct 7, 2016 #3


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    For self study, I suspect successfully doing 80% of the exercises is just fine. I do not have a copy of this book, but it is certainly common for authors to include a portion of exercises that most students cannot do unassisted. I know of texts that include problems that, if solved based on presented material, would indicate a possible Feynman. I even know of one text that includes some unsolved problems as exercises, and another that includes 2 problems that the author knows could not be solved (with a joke based on them: the second is introduced by "for those who solved problem xyz" that cannot be solved);.
    Last edited: Oct 7, 2016
  5. Oct 7, 2016 #4


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    Wald says, in the introduction of his book, that none of the exercises is inordinately difficult, then in parentheses "i.e., I think I can solve them".
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