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 ) .