Scalar Field as a Bose-Einstein Condensate?
  We discuss the analogy between a classical scalar field with a
self-interacting potential, in a curved spacetime described by a quasi--bounded
state, and a trapped Bose-Einstein condensate. In this context, we compare the
Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the
introduction of a curved background spacetime endows, in a natural way, an
equivalence to the Gross-Pitaevskii equation with an explicit confinement
potential. The curvature also induces a position dependent self-interaction
parameter. We exploit this analogy by means of the Thomas-Fermi approximation,
commonly used to describe the Bose-Einstein condensate, in order to analyze the
quasi bound scalar field distribution surrounding a black hole.
