Relativistic formalism to compute quasiequilibrium configurations of nonsynchronized neutron star binaries

A general relativistic version of the Euler equation for perfect fluid hydrodynamics is applied to a system of two neutron stars orbiting each other. In the quasiequilibrium phase of the evolution of this system, a first integral of motion can be derived for certain velocity fields of the neutron star fluid including the (academic) case of corotation with respect to the orbital motion (synchronized binaries) and the realistic case of counter-rotation with respect to the orbital motion. The velocity field leading to this latter configuration can be computed by solving three-dimensional vector and scalar Poisson equations.