Dirac Particles in an Acoustic Black Hole

We investigate the dynamics of spin-1/2 fields in the ( 2 + 1 ) -dimensional draining bathtub spacetime, a well-established analogue model for rotating black holes in hydrodynamic systems. The geometry is characterized by a radial draining parameter A , determining the location of the acoustic horizon, and a circulation parameter B , responsible for frame-dragging effects. We first analyze classical null and timelike geodesics to identify the causal structure, critical orbits, and capture regions of the vortex. Guided by these classical features, we then derive radial solutions of the Dirac equation using the triad formalism for both massless and massive spin-1/2 fermions. The fermionic nature of the field leads to spin-dependent modifications of angular momentum quantization and to distinct superradiant scattering regimes. Conserved Dirac currents and the associated absorption length are computed, allowing us to characterize spin-resolved quantum transport in the analogue black hole background. Our results highlight qualitative differences between scalar and spin-1/2 fermionic fields in vortex geometries and provide experimentally relevant predictions for analogue gravity systems.