We perform simulations of relativistic binary stars in post-Newtonian gravity to investigate their dynamical stability prior to merger against gravitational collapse in a tidal field .
In general , our equations are only strictly accurate to first post-Newtonian order , but they recover full general relativity for spherical , static stars .
We study both corotational and irrotational binary configurations of identical stars in circular orbits .
We adopt a soft , adiabatic equation of state with \Gamma = 1.4 , for which the onset of instability occurs at a sufficiently small value of the compaction M / R that a post-Newtonian approximation is quite accurate .
For such a soft equation of state there is no innermost stable circular orbit , so that we can study arbitrarily close binaries .
This choice still allows us to study all the qualitative features exhibited by any adiabatic equation of state regarding stability against gravitational collapse .
We demonstrate that , independent of the internal stellar velocity profile , the tidal field from a binary companion stabilizes a star against gravitational collapse .