On slow flows of a weakly stratified relativistic fluid in a static gravitational field

Simplified equations for slow flows of a weakly stratified (in entropy) fluid inside or near a massive astrophysical object have been derived from the variational formulation of ideal general relativistic hydrodynamics under the conditions that the gravitational field in the leading order is centrosymmetric and static and that the effect of a magnetic field is negligibly small. Internal waves and vortices in such systems are soft modes as compared to sound. This circumstance allows the formulation of a "soundproof" Hamiltonian model. This model is an analog of nonrelativistic hydrodynamic anelastic models, which are widely used in studies of internal waves and/or convection in spatially inhomogeneous compressible media in atmospheric physics, geophysics, and astrophysics.