Dominant energy condition and superluminal acoustic modes

[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 $$\inline{ p/c^2 < - \rho}$$. 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 $$\inline {dp/d\rho > c^2}$$, which is the (squared) speed of sound of a sound wave.