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Wald General Relativity: On the homogenous cosmology, Page 178

  1. Aug 27, 2013 #1
    Hi, everybody. I have some problem with Wald's statement shown in the picture. This is from the last paragraph in Page 178.

    He claimed that there are only solutions with two of the [itex]p_{\alpha}[/itex] positive and one negative. But it's easy to find out that if two of the [itex]p_{\alpha}[/itex] are negative while the third positive, there is no contradiction.

    Can you guys help me with this? Why should all the solutions have two positive [itex]p_{\alpha}[/itex] and one negative? Thank you:smile:

    (The picture is from http://books.google.com/books?id=9S...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)
     

    Attached Files:

  2. jcsd
  3. Aug 28, 2013 #2

    WannabeNewton

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    Well using (7.2.58) and (7.2.60) we have ##p_2^2 + p_1^2 - p_1 - p_2 + p_1p_2 = 0##. Now if ##p_3 < 0## then ##p_2 > 1 - p_1##. Plot these two and you will find that both ##p_1,p_2 > 0##. If ##p_3 >0## then ##1 - p_1> p_2##; plotting these two again you will find that ##p_1 > 0,p_2 < 0## or vice-versa. Finally if ##p_3 = 0## then either ##p_1 = 1## and ##p_2 = 0## or vice-versa which are just the trivial solutions.
     
  4. Aug 29, 2013 #3
    Thanks! Never thought of this. Great!
     
  5. Aug 29, 2013 #4

    WannabeNewton

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    No problem! Make sure you do the problems at the end of that chapter; some of them are really fun (problems 7.1,7.4, and 7.5 in particular).
     
  6. Aug 29, 2013 #5
    Sure. I'll try to solve all of them before the end of the next week.
     
  7. Aug 29, 2013 #6

    WannabeNewton

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    Awesome, have fun with that!
     
  8. Oct 2, 2013 #7
    Hi WannabeNewton, I know it's been late, but I haven't been able to figure out how to solve the problem 7.4. Can you help me out? Thank you!
     
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