Irrotational binary neutron stars in quasi-equilibrium in general relativity

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.