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

Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena