  In 1973, E. T. Newman considered the holomorphic extension \tilde E(x+iy) of
the Coulomb field E(x) in R^3. By analyzing its multipole expansion, he showed
that the real and imaginary parts of \tilde E(x+iy), viewed as functions of x
for fixed y, are the electric and magnetic fields generated by a spinning ring
of charge R. This represents the electromagnetic part of the Kerr-Newman
solution to the Einstein-Maxwell equations. As already pointed out by Newman
and Janis in 1965, this interpretation is somewhat problematic since the fields
are double-valued. To make them single-valued, a branch cut must be introduced
so that R is replaced by a charged disk D having R as its boundary. In the
context of curved spacetime, D becomes a spinning disk of charge and mass
representing the singularity of the Kerr-Newman solution. Here we confirm the
above interpretation of the real and imaginary parts of \tilde E(x+iy) by
computing the charge- and current densities directly as distributions in R^3
supported in the source disk D. This shows in particular that D spins rigidly
at the critical rate, so that its rim R moves at the speed of light.
  It is a pleasure to thank Ted Newman, Andrzej Trautman and Iwo
Bialinicki-Birula for many instructive discussions, particularly in Warsaw and
during a visit to Pittsburgh.
