  We examine the linear stability of various configurations in Bose-Einstein
condensates with sonic horizons. These configurations are chosen in analogy
with gravitational systems with a black hole horizon, a white hole horizon and
a combination of both. We discuss the role of different boundary conditions in
this stability analysis, paying special attention to their meaning in
gravitational terms. We highlight that the stability of a given configuration,
not only depends on its specific geometry, but especially on these boundary
conditions. Under boundary conditions directly extrapolated from those in
standard General Relativity, black hole configurations, white hole
configurations and the combination of both into a black hole--white hole
configuration are shown to be stable. However, we show that under other (less
stringent) boundary conditions, configurations with a single black hole horizon
remain stable, whereas white hole and black hole--white hole configurations
develop instabilities associated to the presence of the sonic horizons.
