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We present a numerical method to compute quasiequilibrium configurations ofclose binary neutron stars in the pre-coalescing stage. A hydrodynamicaltreatment is performed under the assumption that the flow is either rigidlyrotating or irrotational. The latter state is technically more complicated totreat than the former one (synchronized binary), but is expected to representfairly well the late evolutionary stages of a binary neutron star system. Asregards the gravitational field, an approximation of general relativity isused, which amounts to solving five of the ten Einstein equations (conformallyflat spatial metric). The obtained system of partial differential equations issolved by means of a multi-domain spectral method. Two spherical coordinatesystems are introduced, one centered on each star; this results in a precisedescription of the stellar interiors. Thanks to the multi-domain approach, thishigh precision is extended to the strong field regions. The computationaldomain covers the whole space so that exact boundary conditions are set toinfinity. Extensive tests of the numerical code are performed, includingcomparisons with recent analytical solutions. Finally a constant baryon numbersequence (evolutionary sequence) is presented in details for a polytropicequation of state with gamma=2.Comment: Minor corrections, references updated, 42 pages, 25 PostScript  figures, accepted for publication in Phys. Rev.

Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests