在非保守单模几何中生成精确多方球
Generating exact polytropes in non-conservative unimodular geometries
AI总结：
本文利用无迹 Einstein 方程在静态球对称时空中保留的压力各向同性，通过施加额外约束引入多方球，得到 Tolman-Oppenheimer-Volkoff 型方程，并证明生成的多方星模型物理合理且与观测数据一致。
摘要：
无迹 Einstein 方程比完整场方程少一个方程。在静态且球对称的时空中，场方程的数量因此减少为两个。然而，广义相对论中的压力各向同性方程得以保留，这表明任何已知的完美流体时空都是无迹场景的合适候选者。现在可以利用施加两个约束的额外自由度来引入多方球，这在广义相对论中是很困难的。这里的要点是，使用任何已知的精确解，都可以找到对应多方指数各种值的多方星。人们可以得到 Tolman-Oppenheimer-Volkoff 型方程，并能够显式地研究它们的解。文中讨论了两个著名的恒星分布例子，它们生成的多方球具有物理上合理的行为。这些模型是正规的，表现出永远不会超光速的声速，并且在 Chandrasekhar 意义上是绝热稳定的。我们研究了一种致密性度量，证实我们的结果与某些观测数据一致。
英文摘要：
The trace-free Einstein equations contain one equation less than the complete field equations. In a static and spherically symmetric spacetime, the number of field equations is thus reduced to two. The equation of pressure isotropy of general relativity, however, is preserved thus showing that any known perfect fluid spacetime is a suitable candidate for the trace-free scenario. The extra freedom in imposing two constraints may now be exploited to include polytopes, something that is difficult in general relativity. The point here is that using any known exact solution one can find a polytropic star for various values of the polytropic index. One arrives at Tolman-Oppenheimer-Volkoff type equations and can study their solutions explicitly. Two examples of well-known stellar distributions that generate polytropes with physically reasonable behaviour are discussed. These models are regular, exhibit a sound speed that is never superluminal and are adiabatically stable in the sense of Chandrasekhar. We investigate a compactness measure confirming that our results are consistent with some observational data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
