正压球面星的最大质量
Maximum mass of a barotropic spherical star
摘要：
球形理想流体球的总质量$M$与表面半径$R$之比存在一个上界$M/R < B$。Buchdahl在向外质量密度不增加和正压状态方程的假设下得到了$B = 4/9$。Barraco和Hamity通过在Buchdahl的假设中加入主导能量条件，将Buchdahl的界限降低到较低值$B = 3/8$ $(< 4/9)$。在本文中，我们通过增加亚光速（慢于光速）条件，进一步降低了Barraco-Hamity对$B \simeq 0.3636403$ $(< 3/8)$的束缚。在我们的分析中，我们数值求解Tolman-Oppenheimer-Schmidoff方程，并通过流体球内的质量，半径和压力作为质量密度的函数的变化来最大化质量半径比。
英文摘要：
The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the assumptions; non-increasing mass density in outward direction, and barotropic equation of states. Barraco and Hamity decreased the Buchdahl's bound to a lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease the Barraco-Hamity's bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal (slower-than-light) condition of sound speed. In our analysis, we solve numerically Tolman-Oppenheimer-Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density.
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