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

For certain geometric configurations 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 a consequence of such a 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.