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For three different geometric configurations of matter and two differentthermodynamic equations of state, low angular momentum, multi-transonic,axially symmetric accretion flow of matter having fractional dimension of massdistribution onto a rotating black hole has been studied by employing certainpost-Newtonian pseudo-Kerr black hole potential. Such task has beenaccomplished mathematically by mapping the fractal nature of accreted mediumonto its continuum counterpart. The difference between spin dependence ofaccretion dynamics of the fractal medium and the continuous medium has beenhighlighted. By employing a time dependent linear perturbation scheme, it hasbeen demonstrated that accretion of matter with fractional dimension of densitydistribution can be considered as a natural example of classical analoguemodel. The corresponding acoustic surface gravity has been estimated in termsof accretion variables. The value of the surface gravity changes as theaccreted matter makes a transition from its fractal nature to the correspondingcontinuum distribution.

Axially Symmetric Accretion of Fractal Medium onto Rotating Black Holes and the emergence of the Acoustic Manifold