Vortices without inflow: Bound spectra in horizonless rotational analogs

Analog gravity experiments are making remarkable strides in unveiling both the classical and quantum nature of black holes. By harnessing diverse states of matter, contemporary tabletop setups now replicate strong-field phenomena typically confined to the enigmatic regions surrounding black holes. Through these modern gravity simulators, physical processes once considered elusive may finally be brought into experimental reach. In this work, we investigate the spectrum of massless scalar excitations propagating within the effective geometry of a rotating acoustic metric. Specifically, we build an analog vortex-like spacetime endowed with a tunable parameter that emulates the geometry of a rotating gravitational background. This model accommodates both the presence of a sonic horizon, characteristic of an acoustic black hole for non-zero tuning parameters, and its absence when the parameter vanishes, yielding a horizonless, purely rotational vortex flow devoid of radial inflow. We focus on the case where the vortex flow is purely rotational. The resulting spectral properties is found to be qualitatively consistent with that observed in recent experimental realizations of giant multiply quantum vortices featuring solid or hollow cores. This correspondence suggests that the analog spacetime used here holds significant potential to replicate, qualitatively, the phenomenology of cutting-edge laboratory experiments. In doing so, it offers new insight into the intricate landscape of analog black-hole spectroscopy and, potentially, the resonant topography of bounded, rotating astrophysical environments around black holes.