  We present a numerical scheme that solves the initial value problem in full
general relativity for a binary neutron star in quasi-equilibrium. 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 adopt a quasi-equilibrium approximation. In this
approximation, we integrate a subset of the Einstein equations coupled to the
equations of relativistic hydrodynamics to solve the initial value problem for
binaries of arbitrary separation, down to the innermost stable orbit.
