标题： 一种新的数值方案来计算广义相对论中准平衡致密星的三维构型——同步旋转双星系统应用—— 显示英文标题

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

摘要： 我们开发了一种新的数值方案，以获得非轴对称致密星体（如双中子星系统）及其周围时空的准平衡结构，在广义相对论中。 关于广义相对论中双星系统的准平衡状态，已经有一些研究假设了度规的空间部分的共形平坦性。 然而，除了轴对称配置外，共形平坦处理的有效性尚未得到充分分析。 因此，有必要通过开发与共形平坦方案完全不同的方法来求解准平衡状态。 在本文中，我们提出了一种新的数值方案，直接求解3D配置的爱因斯坦方程，而无需假设共形平坦性，尽管我们使用了简化度规来描述时空。 这种新公式是对之前成功应用于广义相对论中轴对称旋转致密星体结构的方案的扩展。 它基于考虑无限远处边界条件的爱因斯坦方程的积分表示。 我们通过计算牛顿引力中的双流体星系统的平衡序列以及广义相对论中轴对称流体星的平衡序列来验证我们的数值方案。 我们将这个数值代码应用于广义相对论中的双星系统，并成功获得了同步旋转双流体星在多态指数N = 0.0、0.5和1.0下的几个平衡序列。 显示英文摘要

摘要： 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.