纯Lovelock引力下恒星内部的Buchdahl-Vaidya-Tikekar模型- II
Buchdahl-Vaidya-Tikekar model for stellar interior in pure Lovelock gravity - II
摘要：
对于一个给定的Lovelock序$N$，它证明了恒星内部的纯Lovelock方程的静态流体解在所有$n\geq 2N+2$维度上具有相对于适当定义的变量和Vaidya-Tikekar参数$K$的普适行为，表明偏离$3$ -空间几何的球形。我们采用Buchdahl度量分析，其中包括几乎所有已知的物理上可接受的模型，特别是Vaidya-Tikekar和Finch-Skea。此外，对于给定的恒星半径，常密度星，总是由史瓦西内部解描述，定义了最紧凑的分布状态，而另一端则由Finch-Skea模型标记，所有其他物理上成立的模型都位于这两个极限分布之间。
英文摘要：
For a given Lovelock order $N$, it turns out that static fluid solutions of the pure Lovelock equation for a star interior have the universal behavior in all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of $3$-space geometry. We employ the Buchdahl metric ansatz which encompasses almost all the known physically acceptable models including in particular the Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant density star, always described by the Schwarzschild interior solution, defines the most compact state of distribution while the other end is marked by the Finch-Skea model, and all the other physically tenable models lie in between these two limiting distributions.
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