  For certain geometric configuration of matter falling onto a rotating black
hole, we develop a novel linear perturbation analysis scheme to perform the
stability analysis of stationary integral accretion solutions corresponding to
the steady state low angular momentum, inviscid, barotropic, irrotational,
general relativistic accretion of hydrodynamic fluid. We demonstrate that such
steady states remain stable under linear perturbation, and hence the stationary
solutions are reliable to probe the black hole spacetime using the accretion
phenomena.We report that a relativistic acoustic geometry emerges out as the
consequence of such stability analysis procedure. We study various properties
of that sonic geometry in detail. We construct the causal structures to
establish the one to one correspondences of the sonic points with the acoustic
black hole horizons, and the shock location with an acoustic white hole
horizon. The influence of the spin of the rotating black holes on the emergence
of such acoustic spacetime has been discussed.
