准均匀双中子星在一般相对论下的准平衡

双中子星在引力波辐射作用下，以螺旋方式缓慢地相互靠近。在这一过程中，由于引力波辐射耗散能量缓慢，双星预计几乎没有涡旋。事实上， treating the system as having zero vorticity, i.e., as irrotational, is a good approximation. Because the orbital period is much shorter than the radiation reaction time scale, it is also an excellent approximation to treat the system as evolving through a sequence of equilibrium states, in each of which the gravitational radiation is neglected. In Newtonian gravity, one can simplify the hydrodynamic equations considerably for an equilibrium irrotational binary by introducing a velocity potential. The equations reduce to a Poisson-like equation for the potential, and a Bernoulli-type 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.