General Relativistic Stars : Polytropic Equations of State
General Relativistic Stars : Polytropic Equations of State
复制标题
广义相对论恒星:多变状态方程
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
C. Uggla
中科院分区：
文献类型：
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作者：
U. Nilsson;U. Nilsson;C. Uggla
摘要 本文将具有多方状态方程 p=kρ1+1/n 的静态球对称完美流体模型的引力场方程改写为紧状态空间上两个互补的 3 维常微分方程组。使用动力系统理论对系统进行数值和定性分析。某些关键解决方案被显示为形成构建块，这些构建块在很大程度上决定了剩余的解决方案结构。在一种公式中，存在一个单调函数，该函数迫使广义相对论解朝向对应于低压极限的状态空间边界的一部分。该边界上的解描述了牛顿模型，因此清楚地显示了与牛顿解空间的关系。数值证明了广义相对论模型当多变指数n满足0⩽n≲3.339时具有有限半径，当n⩾5时具有无限半径。当3.339≲n时
Abstract In this paper, the gravitational field equations for static spherically symmetric perfect fluid models with a polytropic equation of state, p=kρ1+1/n, are recast into two complementary 3-dimensional regular systems of ordinary differential equations on compact state spaces. The systems are analyzed numerically and qualitatively, using the theory of dynamical systems. Certain key solutions are shown to form building blocks which, to a large extent, determine the remaining solution structure. In one formulation, there exists a monotone function that forces the general relativistic solutions towards a part of the boundary of the state space that corresponds to the low pressure limit. The solutions on this boundary describe Newtonian models and thus the relationship to the Newtonian solution space is clearly displayed. It is numerically demonstrated that general relativistic models have finite radii when the polytropic index n satisfies 0⩽n≲3.339 and infinite radii when n⩾5. When 3.339≲n