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Switching from pressure to energy density on a stress energy tensor

  1. Jul 21, 2009 #1
    the stress energy tensor is defined in my book as |p 0 0 0|
    |0 P 0 0|
    |0 0 P 0|
    |0 0 0 P| where p is the energy density and P is the pressure (momentum flux)
    ...This equation was developed from a very long process which I understand:
    (1) -n[(p+P)/n],_B + P,_B=0 (where ,_B is the beta derivative and my lazy notation, and n is the density)
    Then my book says "A little algebra converts this to"
    (2) -[p,_B -[(p+P)/n)n,_B]=0, notice that the p's switched.
    I can derive the second term of (2) but I cannot figure out how the Pressure changed to energy density. The step before this step switched the equation to its time component, which might have something to do with it but I still do not understand this jump at all.

    It seems to imply that P,_B=-p,_B which is absolutely confusing

    Question: How can one switch a term of the unique stress energy tensor equation for perfect fluids from Pressure,_B to energy density,_B
    (this was taken from page 109 of schutz's first course on general relativity)
     
  2. jcsd
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