What is the relationship between particle and energy frames in fluid dynamics?

[bloby]

Hello.

Is there a way, as for the energy frame, to get the particle frame 4-velocity of a fluid from its energy-momentum tensor?

 

[Bill_K]

Well, you could look for a timelike eigenvector.

 

[bloby]

Could you explain why?

 

[Bill_K]

Quoting Wikipedia: "For a fluid in thermodynamic equilibrium, the stress-energy tensor takes on a particularly simple form
T^αβ = (ρ + p/c²)u^αu^β + p g^αβ where u^α is the fluid's four-velocity."

And clearly u^α is an eigenvector.

 

[bloby]

Ok, but for a fluid out of equillibrium?

 

[Bill_K]

Sorry, I misunderstood. In that case I don't know the answer. Maybe you need to be given more information than just the stress-energy tensor.