  To investigate the possibility that intrinsic gravitational decoherence can
be theoretically demonstrated within canonical quantum gravity, we develop a
model of a self-gravitating interferometer. We search for evidence in the
resulting interference pattern that would indicate coherence is fundamentally
limited due to general relativistic effects. To eliminate the occurence of
gravitational waves, we work in spherical symmetry, and construct the "beam" of
the interferometer out of WKB states for an infinitesimally thin shell of
matter. For internal consistency, we encode information about the beam optics
within the dynamics of the shell itself, by arranging an ideal fluid on the
surface of the shell with an equation of state that enforces beam-splitting and
reflections. We then determine sufficient conditions for (interferometric)
coherence to be fully present even after general relativistic corrections are
introduced, test whether or not they can be satisfied, and remark on the
implications of the results.
