  In this work, we revisit the shear-free conjecture of general relativity and
show the violation of the well-known shear-free condition for perfect-fluid
spacetimes. It had been shown in previous investigations that, in the general
relativistic framework, the matter congruences of shear-free perfect fluid
spacetimes should be either expansion-free or rotation-free. Our current
investigation, however, indicates that a universe dominated by a Chaplygin gas
can allow a simultaneous expansion and rotation of the fluid provided that
certain non-trivial conditions, which we derive and describe below, are met. We
also show that, in the appropriate limiting cases, our results reduce to the
expected results of dust spacetimes which can only expand or rotate, but not
both, at the same time.
