  We construct an electromagnetic field whose scalar potential is a pulsed-beam
wavelet Psi (an analytic continuation of a classical Huygens wavelet). The
vector potential A is determined up to three complex parameters by requiring
that (a) it satisfies the Lorenz gauge condition with Psi, (b) its current
density is supported on the same disk D as the charge density of Psi, (c) it is
axisymmetric, and (d) it has the same retarded time dependence as Psi. By
choosing one of the parameters in A appropriately, the electromagnetic field
generated by the four-potential (A, Psi) can be made null, meaning that E^2=B^2
and E dot B=0. We call such fields coherent because upon being radiated, they
do not loiter around the source, generating electromagnetic inertia (a new
concept related to reactive energy) but immediately propagate out at the speed
of light. The coherent EM wavelets define a twisting null congruence of light
rays in Minkowski space, which we show to be identical to the Kerr congruence
associated with the Kerr-Newman metric. The latter represents a black hole due
to a time-independent charge-current density on a massive disk D spinning at
the angular velocity c/a, where a is the radius of D. By contrast, our coherent
wavelets are electromagnetic pulsed beams radiated by pulsed charge-current
distributions on D, still spinning at the uniform rate c/a.
