Note on aTheorem of Relativistic Hydrodynamics

Author: Krikorian, R.

Source: Astrophysics, Volume 48, Number 4, October 2005 , pp. 539-544(6)

Publisher: Springer

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Abstract:

A well known theorem of relativistic hydrodynamics states that the streamlines of an isentropic perfect fluid are the future-pointing timelike (FPT) curves extremizing the integral J = ∫ _S1 ^S2 fds, where f is the so-called index function and s the proper time on the world line of the fluid particle. The integral is taken over all possible FPT curves with regular representations xⁱ = xⁱ (s) joining the fixed end events E₁, E₂. The purpose of this note is to show that the streamlines of an adiabatic perfect fluid can likewise be regarded as extremizing curves of the functional J provided the class of admissible curves consists of those FPT curves satisfying the side condition uⁱ∂_iS = 0, uⁱ unit 4-velocity and S the specific proper entropy of the fluid, with the first end point fixed and the second being the end point variable.

Keywords: Relativity: hydrodynamics

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10511-005-0052-1

Affiliations: 1: Email: krikorian@iap.fr

Publication date: 2005-10-01