 If we include the effects of the electron's rotation using the Kerr-Newman metric, there is still a naked singularity, which is now a ring singularity, and spacetime also has closed timelike curves.The size of this ring singularity is on the order of

where as before is the electron's mass and is the speed of light, but = formula_1 is the spin angular momentum of the electron.This gives

which is much larger than the length scale associated to the electron's charge.