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

Dark matter condensates as highly nonlocal solitons: instability in the Schwarzschild metric and laboratory analog