  We investigate the variable star content of the isolated, Local Group, dwarf
spheroidal galaxy (dSph) Cetus. Multi-epoch, wide-field images collected with
the VLT/VIMOS camera allowed us to detect 638 variable stars (630 RR Lyrae
stars and 8 Anomalous Cepheids), 475 of which are new detections. We present a
full catalogue of periods, amplitudes, and mean magnitudes. Motivated by the
recent discovery that the pulsational properties of the RR Lyrae stars in the
Tucana dSph revealed the presence of a metallicity gradient within the oldest
(>10 Gyr old) stellar populations, we investigated the possibility of an
analogous effect in Cetus. We found that, despite the obvious radial gradient
in the Horizontal Branch (HB) and Red Giant Branch (RGB) morphologies, both
becoming bluer on average for increasing distance from the center of Cetus, the
properties of the RR Lyrae stars are homogeneous within the investigated area
(out to r~15'), with no significant evidence of a radial gradient. We discuss
this in connection with the star formation history (SFH) previously derived for
the two galaxies. The observed differences between these two systems show that
even systems this small show a variety of early evolutionary histories. These
differences could be due to different merger or accretion histories.
