  Theories on the bosonic nature of dark matter are a promising alternative to
the cold dark matter model. Here we consider a dark matter halo in the state of
a Bose-Einstein condensate, subject to the gravitation of a black hole. In the
low energy limit, we bring together the general relativity in the Schwarzschild
metric and the quantum description of the Bose-Einstein condensate. The model
is solvable in the Fermi normal coordinates with the so called highly nonlocal
approximation and describes tidal deformations in the condensate wave function.
The black hole deforms the localized condensate until the attraction of the
compact object overcomes the self-gravitation and destabilizes the solitonic
dark matter. Moreover, the model can be implemented as a gravitational analog
in the laboratory; the time-dependent potential generated by the galactic black
hole can be mimicked by an optical trap acting on a conventional condensate.
The results open the way to new laboratory simulators for quantum gravitational
effects.
