Researchers have explored the spherically symmetric, general relativistic Michel flow accretion onto black holes, considering an equation of state where the adiabatic index varies with radial distance. This approach has allowed for the construction of stationary integral transonic solutions for multi-component accretion, classifying the nature of the transonic points using dynamical systems theory techniques. The study focuses on how the properties of gas falling into a black hole can give rise to gravity-like phenomena.

The stability of these stationary solutions against linear radial perturbations has been analyzed, finding that the flows are stable. As a result of this stability analysis, the corresponding acoustic spacetime, embedded within the accreting matter, has been derived. Furthermore, the horizon of the metric of this sonic spacetime has been identified by constructing causal structures with Carter-Penrose diagrams. This provides a new perspective on accreting black hole systems.

This work investigates accreting black hole systems from multiple angles: their astrophysical aspects, the dynamical systems point of view, and, crucially, within the realm of classical analogue gravity phenomena. The ability to model and understand the stability of these flows and the emergence of an acoustic spacetime offers a valuable tool for investigating the fundamental properties of gravity in extreme environments, such as those surrounding black holes.