English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle

MPS-Authors
/persons/resource/persons20673

Schutz,  Bernard F.
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
External Organizations;

Locator
There are no locators available
Fulltext (public)

60510.pdf
(Publisher version), 3MB

Supplementary Material (public)
There is no public supplementary material available
Citation

Schutz, B. F. (1970). Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle. Physical Review D, 2(12), 2762-2773. doi:10.1103/PhysRevD.2.2762.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-0F40-5
Abstract
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.