Slow flows of an relativistic perfect fluid in a static gravitational field

TL;DR

This paper studies slow, relativistic perfect fluid flows in a static gravitational field, deriving equations for vortex filament dynamics using variational principles and analyzing quasi-static regimes.

Contribution

It introduces a variational approach to relativistic vortex filament dynamics and examines slow flows with fixed vorticity topology in a gravitational field.

Findings

Derived equations for relativistic vortex filament motion.

Analyzed quasi-static slow flow regimes.

Established a variational principle for vortex line dynamics.

Abstract

Relativistic hydrodynamics of an isentropic fluid in a gravitational field is considered as the particular example from the family of Lagrangian hydrodynamic-type systems which possess an infinite set of integrals of motion due to the symmetry of Lagrangian with respect to relabeling of fluid particle labels. Flows with fixed topology of the vorticity are investigated in quasi-static regime, when deviations of the space-time metric and the density of fluid from the corresponding equilibrium configuration are negligibly small. On the base of the variational principle for frozen-in vortex lines dynamics, the equation of motion for a thin relativistic vortex filament is derived in the local induction approximation.