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Please give me some advise about DEC (dominant energy conditions)

  1. Jun 8, 2005 #1
    DEC is related to superluminal acoustic modes. I can not understand. Help me.

  2. jcsd
  3. Jun 8, 2005 #2


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    A violation of the DEC implies an equation of state [tex]\inline{ p/c^2 < - \rho}[/tex]. You can prove this as follows. Consider first the energy-momentum tensor for a perfect fluid with equation of state [tex]\inline{ \omega p/c^2 = \rho}[/tex]. Take a timelike vector [tex]\inline{ A^{\mu}}[/tex] and calculate [tex]\inline{ T^{\nu}_{\mu} A^{\mu}}[/tex]. The DEC implies that this result must be timelike, but you will see that for w < -1 the DEC must not be satisfied for some [tex]\inline{A^{\mu}}[/tex].

    You can interpret this thinking of a timelike four-velocity [tex]\inline {U^{\mu}}[/tex], which leads to a spacelike energy flow [tex]\inline {T^{\nu}_{\mu} U^{\mu}}[/tex]. Or, also, with this equation of state you can rearrange to [tex]\inline {dp/d\rho > c^2}[/tex], which is the (squared) speed of sound of a sound wave.
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