Document Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars
M. Rieutord and B. Dubrulle (eds)
EAS Publications Series, 21 (2006) 43-79
DOI: 10.1051/eas:2006106
An introduction to relativistic hydrodynamics
E. GourgoulhonLaboratoire de l'Univers et de ses Théories (LUTH), UMR 8102 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France;
eric.gourgoulhon@obspm.fr
Abstract
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