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

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.