  We present the first fully relativistic numerical calculations of
differentially rotating Strange Quark Stars models for broad ranges of the
maximum density and of the degree of differential rotation. Our simulations are
performed with the very accurate and stable multi-domain spectral code FlatStar
and use the MIT Bag model for describing strange quark matter. Our calculations
based on a thorough exploration of the solution space show that the maximum
mass of strange stars depends on both the degree of differential rotation and a
type of solution, similarly to neutron stars described by a polytropic
equations of state. The highest increase of the maximum mass (compared to the
value for a non-rotating star) is obtained for models with a low degree of
differential rotation. This highest mass is over four times larger than that of
the equivalent non rotating configuration. Comparing our results with
calculations done for realistic models of neutron stars, we conclude that with
the help of differential rotation, strange stars can sustain masses much larger
than stars made from nuclear matter for low degree of differential rotation
which reinforces the hope of demonstrating, or of ruling out, the existence of
strange matter through the observation by gravitational waves, by gamma rays or
by neutrinos of the massive material object born from the merger of a compact
binary system or during some supernova events.
