Perfect Fluid Energy Stress Tensor

[alejandrito29]

in a perfect fluid the stress energy tensor is:

T_{AB} = (P + \rho) u_A u_B + P g_{AB}

queation1 : always u_A =1, \vec{0}?

question2: if the space time have a line element h_{AB}dx^A dx^B...for the calculus of T_{AB}, ¿ g_{AB} = h_{AB}?

¿can i to use g_{AB}=\eta_{AB} if h_{AB} \neq \eta_{AB}?

 

[haushofer]

in a perfect fluid the stress energy tensor is:

T_{AB} = (P + \rho) u_A u_B + P g_{AB}

queation1 : always u_A =1, \vec{0}?

No, that's a specific coordinate choice: you're sitting in the rest frame of the fluid's particles.

question2: if the space time have a line element h_{AB}dx^A dx^B...for the calculus of T_{AB}, ¿ g_{AB} = h_{AB}?

This is a bit of a confusing question. If your line element is h_{AB}dx^A dx^B, your metric is h_{AB}; that's how you define your line element. So if there is a metric appearing in your stress tensor, you should take h_{AB}.

That also answers your last question, I guess.