一阶后牛顿近似下的旋转中子星
Rotating neutron stars in the first order post-Newtonian approximation
AI总结：
本研究在钱德拉塞卡建立的后牛顿近似框架下，采用多方物态方程与广义Clement自转定律，开发含两个微扰参数的自洽场迭代数值方法，可有效计算临界自转下中子星的平衡位形。
摘要：
我们在钱德拉塞卡（Chandrasechar）建立的广义相对论后牛顿近似框架内，研究了均匀旋转和较差旋转的中子星模型。具体而言，我们采用多方物态方程以推导相应的流体动力学方程，并采用基于广义Clement模型的自转定律。为计算质量剥离极限（即临界角速度，等价于开普勒角速度）下的平衡位形，我们开发了一种迭代数值方法，该方法属于著名的“自洽场方法”范畴，包含两个微扰参数：“自转参数”$\bar{\u03c5}$与“引力或相对论参数”$\barσ$，分别代表自转和引力对位形的影响。我们通过将所得结果与其他计算方法及公开领域代码的相应结果进行对比，探究了该方法的有效性与适用局限。结果表明，我们的方法能够针对临界自转状态下的广义相对论多方位形得出令人满意的结果。
英文摘要：
We study models of uniformly and differentially rotating neutron stars in the framework of post-Newtonian approximation in general relativity as established by Chandrasechar. In particular, we adopt the polytropic equation of state in order to derive the appropriate hydrodynamic equations and a rotation law based on the generalized Clement's model. To compute equilibrium configurations at the mass-shedding limit, i.e. at critical angular velocity (equivalently, Keplerian angular velocity), we develop an iterative numerical method, belonging to the category of the well-known ``self-consistent field methods'', with two perturbation parameters: the ``rotation parameter'' $\bar{\upsilon}$ and the ``gravitation or relativity parameter'' $\barσ$. These two parameters represent the effects of rotation and gravity on the configuration. We investigate the validity and the limits of our method by comparing our results with respective results of other computational methods and public domain codes. As it turns out, our method can derive satisfactory results for general-relativistic polytropic configurations at critical rotation.
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