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ID: 60510.0, MPI für Gravitationsphysik / Astrophysical Relativity
Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle
Authors:Schutz, Bernard F.
Language:English
Date of Publication (YYYY-MM-DD):1970-12-15
Title of Journal:Physical Review D
Volume:2
Start Page:2762
End Page:2773
Review Status:not specified
Abstract / Description:The equations of hydrodynamics for a perfect fluid in general relativity are cast in Eulerian form, with the four-velocity being expressed in terms of six velocity potentials: U nu =µ-1( phi , nu + alpha beta , nu + theta S, nu ). Each of the velocity potentials has its own "equation of motion." These equations furnish a description of hydrodynamics that is equivalent to the usual equations based on the divergence of the stress-energy tensor. The velocity-potential description leads to a variational principle whose Lagrangian density is especially simple: L=(-g)1 / 2(R+16 pi p), where R is the scalar curvature of spacetime and p is the pressure of the fluid. Variation of the action with respect to the metric tensor yields Einstein's field equations for a perfect fluid. Variation with respect to the velocity potentials reproduces the Eulerian equations of motion
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
External Affiliations:California Institute of Technology, Pasadena, California
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