A new numerical scheme to compute 3D configurations of quasiequilibrium compact stars in general relativity -- Application to synchronously rotating binary star systems --

摘要

We have developed a new numerical scheme to obtain quasiequilibriumstructures of nonaxisymmetric compact stars such as binary neutron star systemsas well as the spacetime around those systems in general relativity. Concerningquasiequilibrium states of binary systems in general relativity, severalinvestigations have been already carried out by assuming conformal flatness ofthe spatial part of the metric. However, the validity of the conformally flattreatment has not been fully analyzed except for axisymmetric configurations.Therefore it is desirable to solve quasiequilibrium states by developingtotally different methods from the conformally flat scheme. In this paper wepresent a new numerical scheme to solve directly the Einstein equations for 3Dconfigurations without assuming conformal flatness, although we make use of thesimplified metric for the spacetime. This new formulation is the extension ofthe scheme which has been successfully applied for structures of axisymmetricrotating compact stars in general relativity. It is based on the integralrepresentation of the Einstein equations by taking the boundary conditions atinfinity into account. We have checked our numerical scheme by computingequilibrium sequences of binary polytropic star systems in Newtonian gravityand those of axisymmetric polytropic stars in general relativity. We haveapplied this numerical code to binary star systems in general relativity andhave succeeded in obtaining several equilibrium sequences of synchronouslyrotating binary polytropes with the polytropic indices N = 0.0, 0.5 and 1.0.