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A question about trace

  1. Jun 17, 2015 #1
    Is there anyone can give me a hand?

    http://arxiv.org/abs/astro-ph/0210603

    203652fk0whw07oq6tk7r0.png
    When I read this paper I can not get Eq.(A.5) from (A.4). Why it is ##4\alpha##? If we take the trace of Eq.(A.4), why not it give us ##6\alpha##?

    Eq. (A.3):
    203656aqmtv95k5kkyknq2.png
    [Edited by a mentor to fix a small problem in the Latex formatting]
     
    Last edited by a moderator: Jun 17, 2015
  2. jcsd
  3. Jun 17, 2015 #2

    fzero

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    The trace of (A.4) is

    $$\delta\hat{h}^r_{ii} + 2 \partial^2 \epsilon = 6 \alpha,$$

    while ##\partial_i\partial_j## gives

    $$ \partial_i\partial_j \hat{h}^r_{ij} + 2 \partial^4 \epsilon = 2 \partial^2\alpha.$$

    Multiplying the 2nd by ##\partial^{-2}## and subtracting gives the first line of (A.5).
     
  4. Jun 18, 2015 #3
    Thank you fzero! Could you please give me some detail? How to get
    $$ \partial_i\partial_j \hat{h}^r_{ij} + 2 \partial^4 \epsilon = 2 \partial^2\alpha.$$
    from
    $$\delta\hat{h}^r_{ii} + 2 \partial^2 \epsilon = 6 \alpha,$$
    And how to get the frist line of (A.5). Actually, I do not understand the "\partial^{-2}". Thank you again.
     
  5. Jun 18, 2015 #4
    Oh, I see. Thank you very much, fzero.
     
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