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

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Homework Help Overview

The discussion revolves around the energy momentum tensor of a perfect fluid in the context of General Relativity. Participants are exploring the derivation of this tensor and the associated action of matter fields.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the existence of a Lagrangian formulation for a perfect fluid and discussing the necessary variables involved, such as particle number density, mass-energy density, pressure, temperature, entropy, and four-velocity. There are references to constraints that arise in such formulations and the lack of a general action.

Discussion Status

Some participants have provided relevant citations and references to literature that discuss the topic further. There appears to be a productive exchange of ideas, with some participants expressing satisfaction with the information shared.

Contextual Notes

There is a note of confusion regarding the appropriate categorization of the question within the forum, indicating a potential misunderstanding of the topic's relevance to the Homework Help section.

smallphi
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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?
 
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However moved that question, it belongs to General Relativity section not to 'Homework and Coursework', geezus ...
 
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
 
Yes, that's what I needed to see. Thanks.
 

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