Neutron stars in binary orbit emit gravitational waves and spiral slowly to
gether. During this inspiral, they are expected to have very little vortici
ty. It is in fact a good approximation to treat the system as having zero v
orticity, i.e., as irrotational. Because the orbital period is much shorter
than the radiation reaction timescale, it is also an excellent approximati
on to treat the system as evolving through a sequence of equilibrium states
, in each of which the gravitational radiation is neglected. In Newtonian g
ravity, one can simplify the hydrodynamic equations considerably for an equ
ilibrium irrotational binary by introducing a velocity potential. The equat
ions reduce to a Poisson-like equation for the potential, and a Bernoulli-t
ype integral for the density. We show that a similar simplification can be
carried out in general relativity. The resulting equations are much easier
to solve than other formulations of the problem.