  Among all electromagnetic theories which (a) are derivable from a Lagrangian,
(b) satisfy the dominant energy condition, and (c) in the weak field limit
coincide with classical linear electromagnetics, we identify a certain subclass
with the property that the corresponding static, spherically symmetric,
asymptotically flat electrovacuum spacetime metric has the mildest possible
singularity at its center, namely, a conical singularity on the time axis. The
electric field moreover has a point defect on the time axis, its total energy
is finite, and is equal to the ADM mass of the spacetime. By an appropriate
scaling of the Lagrangian, one can arrange the total mass and total charge of
these spacetimes to have any chosen values. For small enough mass-to-charge
ratio, these spacetimes have no horizons and no trapped null geodesics. We
prove the uniqueness of these solutions in the spherically symmetric class. We
conclude by performing a qualitative study of the geodesics and test-charge
trajectories of these spacetimes.
