  We set up a model of an elementary electric charge where the noninvertible
metric phase of first order gravity supercedes the standard point singularity.
A topological interpretation of the electric charge is provided in terms of an
index defined for the degenerate spacetime solution, being closely related to
the Euler characteristic. The gravitational equations of motion at this phase
are found to be equivalent to the laws of electrostatics. The associated field
energy is finite and the geometry sourcing the charge is regular.
