Analogue Gravity Models for Planar Black Holes

Abstract: Via constructing an explicit Lagrangian for which the perturbation equations are analogues of a scalar field propagating in a planar black hole space-time, it is found that all planar black holes conformal to a Painlev\'e-Gullstrand type line element can be realized as analogue metrics. This is valid for an arbitrary choice of conformal and blackening factor, thereby vastly extending the number of known examples of explicitly known analogue metrics.