Time domain studies of Active Galactic Nuclei with the Square Kilometre
  Array
  Variability of radio-emitting active galactic nuclei can be used to probe
both intrinsic variations arising from shocks, flares, and other changes in
emission from regions surrounding the central supermassive black hole, as well
as extrinsic variations due to scattering by structures in our own Galaxy. Such
interstellar scattering also probes the structure of the emitting regions, with
microarcsecond resolution. Current studies have necessarily been limited to
either small numbers of objects monitored over long periods of time, or large
numbers of objects but with poor time sampling. The dramatic increase in survey
speed engendered by the Square Kilometre Array will enable precision synoptic
monitoring studies of hundreds of thousands of sources with a cadence of days
or less. Statistics of variability, in particular concurrent observations at
multiple radio frequencies and in other bands of the electromagnetic spectrum,
will probe accretion physics over a wide range of AGN classes, luminosities,
and orientations, as well as enabling a detailed understanding of the
structures responsible for radio wave scattering in the Galactic interstellar
medium.
