An introduction to relativistic hydrodynamics

TL;DR

This paper introduces relativistic hydrodynamics using the Carter-Lichnerowicz approach, emphasizing conservation laws and integrals of motion, useful for modeling relativistic stars and systems without prior GR knowledge.

Contribution

It presents a clear, self-contained introduction to relativistic hydrodynamics based on the Carter-Lichnerowicz approach, highlighting conservation laws and integrals of motion.

Findings

Derivation of relativistic Bernoulli's theorem

Derivation of Kelvin's circulation theorem in relativity

Methods for computing equilibrium configurations of relativistic stars

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.