  Hawking radiation, the spontaneous emission of thermal photons from an event
horizon, is one of the most intriguing and elusive predictions of field theory
in curved spacetimes. A formally analogue phenomenon occurs at the supersonic
transition of a fluid: in this respect, ultracold gases stand out among the
most promising systems but the theoretical modelling of this effect has always
been carried out in semiclassical approximation, borrowing part of the analysis
from the gravitational analogy. Here we discuss the exact solution of a
one-dimensional Bose gas flowing against an obstacle, showing that spontaneous
phonon emission (the analogue of Hawking radiation) is predicted without
reference to the gravitational analogy. Long after the creation of the
obstacle, the fluid settles into a stationary state displaying the emission of
sound waves (phonons) in the upstream direction. A careful analysis shows that
a precise correspondence between this phenomenon and the spontaneous emission
of radiation from an event horizon requires additional conditions to be met in
future experiments aimed at identifying the occurrence of the Hawking-like
mechanism in Bose-Einstein condensates.
