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"Acoustic spacetimes", in which techniques of differential geometry are usedto investigate sound propagation in moving fluids, have attracted considerableattention over the last few decades. Most of the models currently considered inthe literature are based on non-relativistic barotropic irrotational fluids,defined in a flat Newtonian background. The extension, first to specialrelativistic barotropic fluid flow, and then to general relativistic barotropicfluid flow in an arbitrary background, is less straightforward than it might atfirst appear. In this article we provide a pedagogical and simple derivation ofthe general relativistic "acoustic spacetime" in an arbitrary (d+1) dimensionalcurved-space background.

Acoustic geometry for general relativistic barotropic irrotational fluid flow