  This paper presents the derivation of a general solution to the scattering
problem of particles incident onto a barrier of constant potential. This
solution is constructed through a geometrodynamic approach to Bohmian
mechanics, assuming that particles undergo quantum tunneling along geodesic
trajectories in an Alcubierre-type spacetime. Furthermore, from this solution,
mathematical expressions for the quantum potential, momentum, position, and
tunneling time are determined in terms of the spacetime geometry for each
relevant region. This allows us to explain the Hartman effect as a consequence
of spacetime distortion generated by the quantum potential within the barrier.
