  To probe naked spacetime singularities with waves rather than with particles
we study the well-posedness of initial value problems for test scalar fields
with finite energy so that the natural function space of initial data is the
Sobolev space. In the case of static and conformally static spacetimes we
examine the essential self-adjointness of the time translation operator in the
wave equation defined in the Hilbert space. For some spacetimes the classical
singularity becomes regular if probed with waves while stronger classical
singularities remain singular. If the spacetime is regular when probed with
waves we may say that the spacetime is `globally hyperbolic.'
