We perform fully relativistic calculations of binary neutron stars in corotating , circular orbit .
While Newtonian gravity allows for a strict equilibrium , a relativistic binary system emits gravitational radiation , causing the system to lose energy and slowly spiral inwards .
However , since inspiral occurs on a time scale much longer than the orbital period , we can treat the binary to be in quasiequilibrium .
In this approximation , we integrate a subset of the Einstein equations coupled to the relativistic equation of hydrostatic equilibrium to solve the initial value problem for binaries of arbitrary separation .
We adopt a polytropic equation of state to determine the structure and maximum mass of neutron stars in close binaries for polytropic indices n = 1 , 1.5 and 2 .
We construct sequences of constant rest-mass and locate turning points along energy equilibrium curves to identify the onset of orbital instability .
In particular , we locate the innermost stable circular orbit ( ISCO ) and its angular velocity .
We construct the first contact binary systems in full general relativity .
These arise whenever the equation of state is sufficiently soft ( n \stackrel { > } { \sim } 1.5 ) .
A radial stability analysis reveals no tendency for neutron stars in close binaries to collapse to black holes prior to merger .