  We study the dynamics of an atomic BEC subject to local dissipation in the
form of atom losses. We show there is a critical loss rate at which the system
undergoes a continuous dissipative phase transition from a homogenous state
into a state which contains a sonic horizon. The latter drastically alters the
behavior of the system by screening the drain. Dissipation leads to two types
of fluctuations. First, fluctuations are generated by particles emitted in the
reservoir. Both above and below the critical loss, these result in thermal
emission of phonons with a temperature set by the loss rate and the chemical
potential. The second type of fluctuation results from scattering on the drain
and gives rise to a particular correlation pattern that can be observed in the
density-density correlation. Aside from correlations between in an out
scattered modes, outgoing particles are correlated with localized modes through
a process that is reminiscent of Hawking radiation. Finally, we briefly discuss
the dynamics of the system when there are two drains, in which case it is
possible to construct a black hole laser.
