What is the Action of Perfect Fluid in the Energy Momentum Tensor?

In summary, the energy momentum tensor of a perfect fluid can be derived by varying the metric in the action of matter fields. However, there is no general formulation for a complete thermodynamic description of a perfect fluid, but there are proposed action formulations for special cases. These formulations must also force additional constraints. A relevant citation for this is gr-qc/9304026.
  • #1
smallphi
441
2
The energy momentum tensor of perfect fluid is

[itex]T^{\alpha \beta} = \left( \rho + p \right) \, U^\alpha U^\beta - p \, g^{\alpha \beta} [/itex]

It must be derived by varying the metric in the action of matter fields but I've never seen that action. Anyone knows it?
 
Last edited:
Physics news on Phys.org
  • #2
However moved that question, it belongs to General Relativity section not to 'Homework and Coursework', geezus ...
 
  • #3
A relevant citation

smallphi said:
However moved that question, it belongs to General Relativity section not to 'Homework and Coursework', geezus ...

I assume you are asking for a Lagrangian formulation of a complete thermodynamic description of a perfect fluid, i.e. with variables n (particle number density), [itex]rho[/itex] (mass-energy density), p (pressure), T (temperature), s (entropy per particle), and [itex]\vec{U}[/itex] (four-velocity of the fluid) as per MTW. If so, Schutz and Sorkin showed that any such formulation must force additional constraints. That is, there is no general formulation, but there are proposed action formulations for special cases. See for example gr-qc/9304026
 
  • #4
Yes, that's what I needed to see. Thanks.
 

FAQ: What is the Action of Perfect Fluid in the Energy Momentum Tensor?

What is a perfect fluid?

A perfect fluid is a theoretical concept in physics that describes a fluid with no viscosity or internal friction. This means that the fluid flows without any resistance or energy loss.

What are the properties of a perfect fluid?

A perfect fluid has the following properties: it is incompressible, meaning its density remains constant; it is isotropic, meaning its physical properties are the same in all directions; and it is irrotational, meaning it has no vortices or rotational motion.

What is the significance of the action of perfect fluid?

The action of perfect fluid is important in the study of fluid dynamics and cosmology. It helps to explain the behavior of fluids in motion and is used in models of the early universe to understand the expansion and evolution of the cosmos.

How is the action of perfect fluid calculated?

The action of perfect fluid is calculated using the Euler-Lagrange equation, which is a mathematical tool used to find the path of least action for a system. This equation takes into account the kinematic and thermodynamic properties of the fluid, such as its velocity and pressure.

Can a real fluid behave like a perfect fluid?

In reality, there is no such thing as a perfect fluid. All fluids have some level of viscosity and internal friction. However, some fluids, such as water and air, can behave like perfect fluids under certain conditions, such as in low-speed and steady-state flows. These conditions are often approximated in scientific experiments and models.

Similar threads

Is My Calculation of Local Energy Conservation in a Viscous Fluid Correct?
Replies
2
Views
2K
I do not understand stress energy tensor for fluids
Replies
6
Views
1K
Energy-Momentum Tensor of Perfect Fluid
Replies
1
Views
2K
Fluid mechanics: water jet impacting an inclined plane
2
Replies
36
Views
3K
From fluid energy conservation equation to the continuity equation
Replies
5
Views
1K
Orthogonal Projection of Perfect Fluid Energy Momentum
Replies
1
Views
2K
Deriving perfect fluid energy tensor from point particles
Replies
5
Views
3K
Why is solid density used in this thermodynamics problem?
Replies
5
Views
1K
Divergence of the energy momentum tensor
Replies
1
Views
4K
Transforming Stress-Energy Tensors in Different Frames
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top