  We study the dynamical stability against bar-mode deformation of rapidly and
differentially rotating stars in the first post-Newtonian approximation of
general relativity. We vary the compaction of the star $M/R$ (where $M$ is the
gravitational mass and $R$ the equatorial circumferential radius) between 0.01
and 0.05 to isolate the influence of relativistic gravitation on the
instability. For compactions in this moderate range, the critical value of
$\beta \equiv T/W$ for the onset of the dynamical instability (where $T$ is the
rotational kinetic energy and $W$ the gravitational binding energy) slightly
decreases from $\sim 0.26$ to $\sim 0.25$ with increasing compaction for our
choice of the differential rotational law. Combined with our earlier findings
based on simulations in full general relativity for stars with higher
compaction, we conclude that relativistic gravitation {\em enhances} the
dynamical bar-mode instability, i.e. the onset of instability sets in for
smaller values of $\beta$ in relativistic gravity than in Newtonian gravity. We
also find that once a triaxial structure forms after the bar-mode perturbation
saturates in dynamically unstable stars, the triaxial shape is maintained, at
least for several rotational periods. To check the reliability of our numerical
integrations, we verify that the general relativistic Kelvin-Helmholtz
circulation is well-conserved, in addition to rest-mass energy, total
mass-energy, linear and angular momentum. Conservation of circulation indicates
that our code is not seriously affected by numerical viscosity. We determine
the amplitude and frequency of the quasi-periodic gravitational waves emitted
during the bar formation process using the quadrupole formula.
