  In this diplom-arbeit I consider a specific class of "analogue models" of
curved spacetime that are specifically based on the use of Bose-Einstein
condensates.
  As is usual in "analogue models", we are primarily interested in the
kinematics of fields and quanta immersed in a curved-space background. We are
not directly concerned with the Einstein equations of general relativity. Over
the last few years numerous papers concerning "analogue models" have been
published, the key result being that in many dynamical systems the
perturbations have equations of motion that are governed by an "effective
metric" that can often be interpreted in terms of an equivalent gravitational
field.
  After a brief introduction concerning Bose-Einstein condensates and general
relativity, I explain the connection between these two fields. Several specific
examples are then explored in a little more detail:
  1) Sinks and acoustic black holes [dumb holes].
  2) Ring-shaped Laval nozzles and acoustic horizons.
  3) the de Sitter universe.
  In particular, the de Sitter universe is modelled by a freely expanding
condensate obtained by suddenly switching off the trap that normally holds the
condensate in place.
