  Time-series data taken with the Hubble Space Telescope of a field six core
radii (~5') from the center of the globular cluster Messier 4, and covering a
period of about 10 weeks in early 2001, have been analyzed in search of
variable objects. Various criteria were employed to select candidate variable
stars. Period searches were performed on the selected candidates using phase
dispersion minimization (PDM). The reliability of the PDM search results was
tested using synthetic light curves of eclipsing binary stars and sinusoidal
light curves of different periods. Results from this analysis showed that there
are probably no eclipsing binary stars or periodic variables in our field with
periods on the order of a few hours to a few days, down to limiting magnitudes
of V~25 and I~24, which is consistent with the absence of contact binaries such
as W Ursae Majoris systems. However, one candidate variable star does show an
increase in brightness of ~0.1 magnitudes in both bandpasses, which seems to
last for a few days. Possible explanations concerning the nature of this object
include a binary system with a white dwarf primary and a low-mass main sequence
secondary, or a BY Draconis variable star. We are able to set an upper limit to
the observed fraction of photometric variability in this dataset of 0.05%.
