EAS Publications Series
Volume 21, 2006Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars
|Page(s)||43 - 79|
|Published online||07 June 2006|
M. Rieutord and B. Dubrulle (eds)
EAS Publications Series, 21 (2006) 43-79
An introduction to relativistic hydrodynamics
Laboratoire de l'Univers et de ses Théories (LUTH),
UMR 8102 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France
Corresponding author: email@example.com
This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading very straightforwardly to important conservation laws, such as the relativistic generalizations of Bernoulli's theorem or Kelvin's circulation theorem. It also permits to get easily first integrals of motion which are particularly useful for computing equilibrium configurations of relativistic stars in rotation or in binary systems. The presentation is relatively self-contained and does not require any a priori knowledge of general relativity. In particular, the three types of derivatives involved in relativistic hydrodynamics are introduced in detail: this concerns the Lie, exterior and covariant derivatives.
© EAS, EDP Sciences, 2006
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