Energy stress tensor

  • #1
in a perfect fluid the stress energy tensor is:

[tex] T_{AB} = (P + \rho) u_A u_B + P g_{AB} [/tex]

queation1 : always [tex]u_A =1, \vec{0}? [/tex]

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

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

Answers and Replies

  • #2
haushofer
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in a perfect fluid the stress energy tensor is:

[tex] T_{AB} = (P + \rho) u_A u_B + P g_{AB} [/tex]

queation1 : always [tex]u_A =1, \vec{0}? [/tex]
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 [tex] h_{AB}dx^A dx^B[/tex]...for the calculus of [tex]T_{AB}[/tex], [tex]¿ g_{AB} = h_{AB}?[/tex]
This is a bit of a confusing question. If your line element is [tex]h_{AB}dx^A dx^B[/tex], your metric is [tex] h_{AB}[/tex]; that's how you define your line element. So if there is a metric appearing in your stress tensor, you should take [tex]h_{AB}[/tex].

That also answers your last question, I guess.
 

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