  Mesoscopic effects associated with wave propagation in spacetime with metric
stochasticity are studied. We show that the scalar and spinor waves in a
stochastic spacetime behave similarly to the electrons in a disordered system.
Viewing this as the quantum transport problem, mesoscopic fluctuations in such
a spacetime are discussed. The conductance and its fluctuations are expressed
in terms of a nonlinear sigma model in the closed time path formalism. We show
that the conductance fluctuations are universal, independent of the volume of
the stochastic region and the amount of stochasticity.
