  We have developed a new numerical scheme to obtain quasiequilibrium
structures of nonaxisymmetric compact stars such as binary neutron star systems
as well as the spacetime around those systems in general relativity. Concerning
quasiequilibrium states of binary systems in general relativity, several
investigations have been already carried out by assuming conformal flatness of
the spatial part of the metric. However, the validity of the conformally flat
treatment has not been fully analyzed except for axisymmetric configurations.
Therefore it is desirable to solve quasiequilibrium states by developing
totally different methods from the conformally flat scheme. In this paper we
present a new numerical scheme to solve directly the Einstein equations for 3D
configurations without assuming conformal flatness, although we make use of the
simplified metric for the spacetime. This new formulation is the extension of
the scheme which has been successfully applied for structures of axisymmetric
rotating compact stars in general relativity. It is based on the integral
representation of the Einstein equations by taking the boundary conditions at
infinity into account. We have checked our numerical scheme by computing
equilibrium sequences of binary polytropic star systems in Newtonian gravity
and those of axisymmetric polytropic stars in general relativity. We have
applied this numerical code to binary star systems in general relativity and
have succeeded in obtaining several equilibrium sequences of synchronously
rotating binary polytropes with the polytropic indices N = 0.0, 0.5 and 1.0.
