  The time-variable electromagnetic sky has been well-explored at a wide range
of wavelengths. Numerous high-energy space missions take advantage of the dark
Gamma-ray and X-ray sky and utilize very wide field detectors to provide almost
continuous monitoring of the entire celestial sphere. In visible light, new
wide-field ground-based surveys cover wide patches of sky with ever decreasing
cadence, progressing from monthly-weekly time scale surveys to sub-night
sampling. In the radio, new powerful instrumentation offers unprecedented
sensitivity over wide fields of view, with pathfinder experiments for even more
ambitious programs underway. In contrast, the ultra-violet (UV) variable sky is
relatively poorly explored, even though it offers exciting scientific
prospects. Here, we review the potential scientific impact of a wide-field UV
survey on the study of explosive and other transient events, as well as known
classes of variable objects, such as active galactic nuclei and variable stars.
We quantify our predictions using a fiducial set of observational parameters
which are similar to those envisaged for the proposed ULTRASAT mission. We show
that such a mission would be able to revolutionize our knowledge about massive
star explosions by measuring the early UV emission from hundreds of events,
revealing key physical parameters of the exploding progenitor stars. Such a
mission would also detect the UV emission from many tens of tidal-disruption
events of stars by super massive black holes at galactic nuclei and enable a
measurement of the rate of such events. The overlap of such a wide-field UV
mission with existing and planned gravitational-wave and high-energy neutrino
telescopes makes it especially timely.
