Spinning black hole in a fluid

In this paper, we propose a new analog gravity example-a spinning (or Kerr) black hole in an extended fluid model; the latter was derived in an earlier work [A. K. Mitra and S. Ghosh, Divergence anomaly and Schwinger terms: Towards a consistent theory of anomalous classical fluids, Phys. Rev. D 106, L041702 (2022).] by two of the present authors. The fluid model receives Berry curvature contributions and applies to electron dynamics in condensed matter lattice systems in the hydrodynamic limit. We construct the acoustic metric for sonic fluctuations that obey a structurally relativistic wave equation in an effective curved background. In a novel approach of dimensional analysis, we have derived explicit expressions for effective mass and angular momentum per unit mass in the acoustic metric (in terms of fluid parameters), to identify with corresponding parameters of the Kerr metric. The spin is a manifestation of the Berry curvature -induced effective noncommutative structure in the fluid. Finally we put the Kerr black hole analogy in a robust setting by revealing explicitly the presence of horizon and ergoregion for a specific background fluid velocity profile. We also show that near horizon behavior of the phase -space trajectory of a probe particle agrees with Kerr black hole analogy. In a fluid dynamics perspective, the presence of a horizon signifies the wave blocking phenomenon.