Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
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DOI：
10.1103/physrevd.70.044044
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发表时间：
2004-07
影响因子：
5
通讯作者：
M. Shibata;K. Uryū;J. Friedman
中科院分区：
文献类型：
--
作者：
M. Shibata;K. Uryū;J. Friedman
维里关系{M}{MATHROM{ADM}}{=M}{\MATHROM{K}}$和形式为$\ensuremath{\delta}{M}_{\mathrm{ADM}}=\ensuremath{\Omega}\ensuremath{\delta}J，$的第一定律应由描述准平衡圆轨道上的二元致密物体的解和解序列来满足。这里，${M}_{\mathm{adm}}、$${M}_{\mathm{K}}、$J和$\ensureath{\omegga}分别是Arnowitt-Deser-Misner(ADM)质量、Komar质量、角动量和轨道角速度。$\ensureath{\增量}$表示欧拉变种。这两个条件限制了我们可能采用的允许的配方。首先，对于一般渐近平坦的时空，我们得到了${M}_{\mathm{adm}}$与${M}_{\mathm{K}}$之间的关系，以及$\ensureath{\Delta}{M}_{\mathm{adm}}$与$\ensureath{\omga}\ensureath{\Delta}J$之间的关系。然后，为了得到满足维里关系的解和至少近似满足第一定律的解序列，我们提出了广义相对论中准平衡双中子星的计算公式。与以前求解部分爱因斯坦方程的方法不同，在新的公式中，整个爱因斯坦方程是用最大切片和共形三度规的横向规范来求解的。在近区施加了螺旋对称，而在远区则假定为无波长条件。我们期望在这个公式中得到的解是极好的准平衡，并为双星中子星合并的数值模拟提供初始数据。
Two relations, the virial relation ${M}_{\mathrm{ADM}}{=M}_{\mathrm{K}}$ and the first law in the form $\ensuremath{\delta}{M}_{\mathrm{ADM}}=\ensuremath{\Omega}\ensuremath{\delta}J,$ should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, ${M}_{\mathrm{ADM}},$ ${M}_{\mathrm{K}},$ J, and $\ensuremath{\Omega}$ are the Arnowitt-Deser-Misner (ADM) mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $\ensuremath{\delta}$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between ${M}_{\mathrm{ADM}}$ and ${M}_{\mathrm{K}}$ and between $\ensuremath{\delta}{M}_{\mathrm{ADM}}$ and $\ensuremath{\Omega}\ensuremath{\delta}J$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.