  We present results of numerical computations of quasiequilibrium sequences of
binary neutron stars with zero vorticity, in the general relativistic
framework. The Einstein equations are solved under the assumption of a
conformally flat spatial 3-metric (Wilson-Mathews approximation). The evolution
of the central density of each star is monitored as the orbit shrinks in
response to gravitational wave emission. For a compactification ratio M/R=0.14,
the central density remains rather constant (with a slight increase, below
0.1%) before decreasing. For a higher compactification ratio M/R=0.17 (i.e.
stars closer to the maximum mass configuration), a very small density increase
(at most 0.3%) is observed before the decrease. This effect remains within the
error induced by the conformally flat approximation. It can be thus concluded
that no substantial compression of the stars is found, which would have
indicated a tendency to individually collapse to black hole prior to merger.
Moreover, no turning point has been found in the binding energy or angular
momentum along evolutionary sequences, which may indicate that these systems do
not have any innermost stable circular orbit (ISCO).
