  The idea of defining a gravitational singularity as an obstruction to the
dynamical evolution of a test field (described by a PDE) rather than the
dynamical evolution of a particle (described by a geodesics) is explored. In
particular, the concept of field regularity is introduced which serves to
describe the well-posedness of the local initial value problem for a given
field.In particular this is applied to (classical) scalar fields in the class
of curve integrable spacetimes to show that the classical singularities do not
interrupt the well-posedness of the wave equation.
