  We perform some numerical study of the secular triaxial instability of
rigidly rotating homogeneous fluid bodies in general relativity. In the
Newtonian limit, this instability arises at the bifurcation point between the
Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by
viscous dissipation. We locate the onset of instability along several constant
baryon mass sequences of uniformly rotating axisymmetric bodies for compaction
parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi
like bar mode instability, but the stabilizing effect is not very strong.
According to our analysis the critical value of the ratio of the kinetic energy
to the absolute value of the gravitational potential energy $(T/|W|)_{\rm
crit}$ for compaction parameter as high as 0.275 is only 30% higher than the
Newtonian value. The critical value of the eccentricity depends very weakly on
the degree of relativity and for $M/R=0.275$ is only 2% larger than the
Newtonian value at the onset for the secular bar mode instability. We compare
our numerical results with recent analytical investigations based on the
post-Newtonian expansion.
