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Motivated by the need to conceive freely-precessing gyroscopes for detectingacoustic frame-dragging predicted recently in rotating acoustic analogue blackholes, we report an incipient investigation on the hydrodynamics of nematicactive fluids. With a specific assumption on barotropicity of a nematic fluid,we discern acoustic analogue black hole spacetimes experienced by linearperturbations of the velocity potential. For vanishingly small diffusivity ofthe active particles, linear perturbations of the active particle concentrationreveal a profile with an enhancement close to the acoustic horizon, hintingtowards the possibility of partial trapping of active matter by the acousticblack hole. We further show that, as anticipated, the dynamical nature of theorientation (`polarization') of individual particles indeed opens up thepossibility of their use as freely-precessing gyroscopes. In addition,inclusion of diffusivity of active particles in the inviscid solvent is shownto lead to a small effective viscosity. Depending on the sign of the diffusioncoefficient, this can either yield superfluid-like behaviour, or enhance thenet viscosity, of the nematic system. In either situation, acousticsuperradiance, theoretically analyzed and experimentally observed recently formildly viscous standard fluids, is thus predicted to occur for nematic fluids.

Bacteria Around an Acoustic Black Hole: Trapping and Frame-Dragging