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

[ylping]

DEC is related to superluminal acoustic modes. I can not understand. Help me.

Thanks.

 

[hellfire]

A violation of the DEC implies an equation of state \inline{ p/c^2 &lt; - \rho}. You can prove this as follows. Consider first the energy-momentum tensor for a perfect fluid with equation of state \inline{ \omega p/c^2 = \rho}. Take a timelike vector \inline{ A^{\mu}} and calculate \inline{ T^{\nu}_{\mu} A^{\mu}}. 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 \inline{A^{\mu}}.

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