Quasibound modes of rotating acoustic black holes

In this paper, we introduce a metric describing rotating acoustic black holes in spherical coordinates. This formulation allows us to obtain exact analytical solutions of the massless Klein--Gordon equation governing scalar perturbations in the corresponding background spacetime. By imposing the appropriate boundary conditions, we derive an exact analytical expression for the quasibound state frequencies of the system. Quasibound states play a central role in the dynamics of black hole analog systems, as they characterize long-lived resonant modes trapped in the vicinity of the effective horizon. Their investigation provides valuable insights into wave propagation, mode stability, and energy confinement in analog spacetimes. Moreover, because acoustic black holes offer experimentally accessible realizations of horizon physics, the study of quasibound states may establish a direct connection between theoretical predictions and laboratory observations, thereby contributing to a deeper understanding of phenomena that also arise in gravitational black hole environments.