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I Trick for Remembering Schwarzschild Christoffel's/EFE's?

  1. Jul 9, 2016 #1
    Anybody have a stupid/intuitive/clever trick/mnemonic/baby-story to remember the Christoffel symbols

    nP7No.png

    and the Einstein Field equations

    FYju7.png

    for the Schwarzschild metric

    $$ds^2 = A(r)dt^2 - B(r)dr^2 - r^2 d \theta^2 - r^2 \sin^2(\theta) d\varphi^2$$

    without even using a pen? I can derive it all multiple ways etc... but writing these things down from thin air from memory without any effort is the next hurdle, any tricks appreciated :cool:
     
    Last edited by a moderator: Jul 10, 2016
  2. jcsd
  3. Jul 9, 2016 #2

    PeterDonis

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    2016 Award

    Staff: Mentor

    The signs here are not correct. If the ##dt^2## term is positive then all the other terms need to be negative. (Or vice versa.)

    As for mnemonics, I just use a symbolic math package (Maxima and GRTensor in my case) and let it do the grunt work. :wink:
     
  4. Jul 10, 2016 #3
    Thanks, can't edit, meant to write

    $$ds^2 = A(r)dt^2 - B(r)dr^2 - r^2 d\theta^2 - r^2 \sin^2(\theta) d \psi^2$$
     
  5. Jul 10, 2016 #4

    PeterDonis

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    2016 Award

    Staff: Mentor

    I used magic moderator powers to edit the OP and fix the signs. I also corrected the ##\psi## to a ##\varphi## to match the rest of the post.
     
  6. Jul 10, 2016 #5
    Ah even the $$\psi$$ was off, now you see why I want tricks to remember this stuff :-p
     
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