  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.
