Perfect Fluid Energy Stress Tensor

You're free to use whatever metric appears in your line element, but you have to be consistent. If h_{AB} \neq \eta_{AB}, then you have to use h_{AB} in your stress tensor, not \eta_{AB}.In summary, in a perfect fluid the stress energy tensor is T_{AB} = (P + \rho) u_A u_B + P g_{AB}. If the space-time has a line element h_{AB}dx^A dx^B, then the metric used in the stress tensor should also be h_{AB}. The metric used in the stress tensor should be consistent with the line element, regardless of whether it is equal to \eta_{AB} or not
  • #1
alejandrito29
150
0
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]
 
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  • #2
alejandrito29 said:
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.
 

Related to Perfect Fluid Energy Stress Tensor

1. What is a Perfect Fluid Energy Stress Tensor?

A Perfect Fluid Energy Stress Tensor is a mathematical concept used in physics to describe the energy and momentum of a perfect fluid. It is a 4x4 matrix that represents the energy density, pressure, and flow of a fluid in a given space and time.

2. How is a Perfect Fluid Energy Stress Tensor calculated?

A Perfect Fluid Energy Stress Tensor is calculated using the equations of fluid dynamics, which take into account the fluid's density, velocity, and pressure. It can also be derived from the energy-momentum tensor in general relativity.

3. What are the properties of a Perfect Fluid Energy Stress Tensor?

Some key properties of a Perfect Fluid Energy Stress Tensor include conservation of energy and momentum, isotropy, and the absence of shear stresses. It also follows the law of energy conservation and satisfies the equations of motion for a perfect fluid.

4. What is the significance of a Perfect Fluid Energy Stress Tensor?

A Perfect Fluid Energy Stress Tensor is a useful tool for studying the behavior of fluids in various physical systems, such as in astrophysics, cosmology, and fluid mechanics. It is also important in understanding the behavior of matter in extreme conditions, such as in black holes or the early universe.

5. Are there real-world applications of the Perfect Fluid Energy Stress Tensor?

Yes, the Perfect Fluid Energy Stress Tensor has many real-world applications, such as in the study of fluid dynamics and turbulence, the behavior of materials under extreme conditions, and the modeling of astrophysical phenomena. It is also used in the development of technologies such as fluid pumps and turbines.

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