Stability of relativistic Bondi accretion in Schwarzschild-(anti-)de Sitter spacetimes

In a recent paper we investigated stationary, relativistic Bondi-type accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their stability, using the method developed by Moncrief. The analysis applies to perturbations satisfying the potential flow condition. We prove that global isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable, assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de Sitter geometries and polytropic flows in Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary conditions.