  Astrophysical black holes are generally surrounded by accretion disks,
galactic matter and the omnipresent cosmic microwave background radiation, thus
allowing for the concurrent propagation of both gravitational and sound waves.
Recently, acoustic black holes were embedded in Schwarzschild spacetime
allowing for the coexistence of event and acoustic horizons. Here, we obtain a
class of perturbative solutions to the field equations of the relativistic
Gross-Pitaevskii and Yang-Mills theories, which describe sound waves
propagating on a curved slowly-rotating acoustic black hole, akin to
Lense-Thirring spacetime. We investigate the quasinormal mode frequencies,
Hawking-Unruh radiation, and quasibound states. Our novel metric mimics the
gravitational field of astrophysical compact objects in the limiting case of
slow rotation, and therefore could, in principle, shed more light into the
underlying classical and quantum physics of black holes through analog acoustic
probes.
