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

## TL;DR

This paper investigates how fractal, axially symmetric accretion flows onto rotating black holes behave under different conditions, highlighting differences from continuous media and exploring their acoustic analogues.

## Contribution

It introduces a mathematical framework for modeling fractal accretion onto rotating black holes and analyzes the resulting acoustic geometry and surface gravity.

## Key findings

- Fractal accretion dynamics differ from continuous media depending on black hole spin.
- Acoustic surface gravity varies with the transition from fractal to continuum distribution.
- The study demonstrates the natural emergence of classical analogue models from fractal accretion flows.

## Abstract

For three different geometric configurations of matter and two different thermodynamic equations of state, low angular momentum, multi-transonic, axially symmetric accretion flow of matter having fractional dimension of mass distribution onto a rotating black hole has been studied by employing certain post-Newtonian pseudo-Kerr black hole potential. Such task has been accomplished mathematically by mapping the fractal nature of accreted medium onto its continuum counterpart. The difference between spin dependence of accretion dynamics of the fractal medium and the continuous medium has been highlighted. By employing a time dependent linear perturbation scheme, it has been demonstrated that accretion of matter with fractional dimension of density distribution can be considered as a natural example of classical analogue model. The corresponding acoustic surface gravity has been estimated in terms of accretion variables. The value of the surface gravity changes as the accreted matter makes a transition from its fractal nature to the corresponding continuum distribution.