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An introduction to relativistic hydrodynamics

Published online by Cambridge University Press:  07 June 2006

E. Gourgoulhon*
Affiliation:
Laboratoire de l'Univers et de ses Théories (LUTH), UMR 8102 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France
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Abstract

This lecture provides some introduction to perfect fluid dynamics within theframework of general relativity. The presentation is based on theCarter-Lichnerowicz approach. It has the advantage over the more traditionalapproach of leading very straightforwardly to important conservation laws, such as the relativistic generalizations ofBernoulli's theorem or Kelvin's circulation theorem. It also permits to get easily first integrals of motion which are particularly usefulfor computing equilibrium configurations of relativistic stars in rotation or in binary systems.The presentation is relatively self-contained and does not require any a prioriknowledge of general relativity. In particular, the three types of derivatives involved in relativistic hydrodynamics are introducedin detail: this concerns the Lie, exterior and covariant derivatives.

Type
Research Article
Copyright
© EAS, EDP Sciences, 2006

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