  We study the passive influence of quantum matter fluctuations on the
expansion parameter of a congruence of timelike geodesics in a semiclassical
regime. In particular, we show that, the perturbations of this parameter can be
considered to be elements of the algebra of matter fields at all perturbative
order. Hence, once a quantum state for matter is chosen, it is possible to
explicitly evaluate the behavior of geometric fluctuations. After introducing
the formalism necessary to treat similar problems, in the last part of the
paper, we estimate the approximated probability of having a geodesic collapse
in a flat spacetime due to those fluctuations.
