# Energy stress tensor

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 $$h_{AB} \neq \eta_{AB}?$$

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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 $$h_{AB}$$.