  The current article explores the problem of a Bose-Einstein condensate (BEC)
trapped in an anisotropic three-dimensional harmonic-oscillator potential, with
positive effective interatomic interactions, and the analogue gravity acoustic
metric emerging from it. We find that the latter gives rise to a family of
conformally equivalent metrics and the space-time interval corresponds to that
of an accelerated observer subject to a position-dependent acceleration.
Furthermore, such acceleration can be deduced differentiating the potential of
the trap, which leads us to infer that, for a Bose-Einstein condensate in an
arbitrary trap, the space-time interval will correspond to the conformal
equivalent of that of an accelerated observer, being the acceleration in any
direction proportional to the partial derivative of the trap potential of the
BEC with respect to that coordinate. Finally, we compute the space-time
interval, the Einstein tensor and the geodesic equations, identifying some of
the Killing vectors, for three cases: the spherically symmetric, the axially
symmetric and the asymmetric traps.
