  Analogue spacetimes can be used to probe and study physically interesting
spacetime geometries by constructing, either theoretically or experimentally,
some notion of an effective Lorentzian metric
$[g_\mathrm{eff}(g,V,\,\Xi)]_{ab}$. These effective metrics generically depend
on some physical background metric $g_{ab}$, often flat Minkowski space
$\eta_{ab}$, some "medium" with 4-velocity $V^a$, and possibly some additional
background fields $\Xi$. Electromagnetic analogue models date back to the
1920s, acoustic analogue models to the 1980s, and BEC-based analogues to the
1990s. The acoustic analogue models have perhaps the most rigorous mathematical
formulation, and these acoustic analogue models really work best in the absence
of vorticity, if the medium has an irrotational flow. This makes it difficult
to model rotating astrophysical spacetimes, spacetimes with non-zero angular
momentum, and in the current article we explore the extent to which one might
hope to be able to model astrophysical spacetimes with angular momentum,
(thereby implying vorticity in the 4-velocity of the medium).
