  We apply the topological quantization method to some gravitational fields
which can be represented as generalized harmonic maps. This representation
extends the well-known concept of harmonic maps and allows us to describe some
solutions to the Einstein field equations as generalized strings, where the
base space for the generalized harmonic map is a two-dimensional manifold. The
results obtained here point to an incompatibility of the classical description
of the gravitational field and its symmetries with a discretization of the
parameters that enter in its description.
