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New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state

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arxiv 1209.2754 v1 pith:J3UC72MU submitted 2012-09-12 gr-qc astro-ph.COmath-phmath.MP

Olivier Minazzoli , Tiberiu Harko This is my paper · ORCID
classification gr-qcastro-ph.COmath-phmath.MP
keywords fluidlagrangianbarotropicconservedderivationnumberparticleperfect
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abstract

In this paper we give a simple proof that when the particle number is conserved, the Lagrangian of a barotropic perfect fluid is $\mathcal{L}_m=-\rho [c^2 +\int P(\rho)/\rho^2 d\rho]$, where $\rho$ is the \textit{rest mass} density and $P(\rho)$ is the pressure. To prove this result nor additional fields neither Lagrange multipliers are needed. Besides, the result is applicable to a wide range of theories of gravitation. The only assumptions used in the derivation are: 1) the matter part of the Lagrangian does not depend on the derivatives of the metric, and 2) the particle number of the fluid is conserved ($\nabla_\sigma (\rho u^\sigma)=0$).

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Cited by 6 Pith papers

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