On the stability of steady general-relativistic accretion and analogue black holes

Investigation of general-relativistic spherically symmetric steady accretion of self-gravitating perfect fluid onto compact objects reveals the existence of two weakly accreting regimes. In the first (corresponding to the test fluid approximation) the mass of the central object is much larger than the mass of the accreting fluid; in the second the mass of the fluid dominates. The stability of the solutions belonging to the first regime has been proved by Moncrief. In this work we report the results of a series of numerical studies demonstrating stability of massive solutions, i.e., belonging to the second of the aforementioned regimes. It is also shown that a formal analogy between "sonic horizons" in the accretion picture and event horizons in general relativity is rather limited. The notion of a "sonic horizon" is only valid in a linear regime of small hydrodynamical perturbations. Strong perturbations can still escape from beneath the "sonic horizon."