论文标题
静态球形完美流体星，具有有限半径的一般相对论：评论
Static spherical perfect fluid stars with finite radius in general relativity: a review
论文作者
论文摘要
在本文中，我们对Tolman-Oppenheimer-Volkoff（TOV）方程及其解决方案进行了教学评论，该方程描述了一般相对性中静态的，球体对称的气体恒星。我们的讨论始于来自爱因斯坦场方程和相对论欧拉方程的TOV方程的系统推导。接下来，我们给出了描述有限半径之星的TOV方程解决方案的存在和独特性的证明，假设在表征气体的状态方程上有适当的条件。我们还证明，以原点为中心的球体内部的气体的紧凑性满足了众所周知的buchdahl结合，而与球体的半径无关。此外，我们从统计力学考虑的理想，经典的单元相对论气体中得出了状态方程，并表明它满足了我们对存在描述有限半径恒星的独特解决方案的假设。尽管本文中讨论的结果都不是新的，但它们通常散布在文献中的不同文章和书籍中。因此，我们希望本文将对相对论恒星模型的主题提供独立且有用的介绍。
In this article, we provide a pedagogical review of the Tolman-Oppenheimer-Volkoff (TOV) equation and its solutions which describe static, spherically symmetric gaseous stars in general relativity. Our discussion starts with a systematic derivation of the TOV equation from the Einstein field equations and the relativistic Euler equations. Next, we give a proof for the existence and uniqueness of solutions of the TOV equation describing a star of finite radius, assuming suitable conditions on the equation of state characterizing the gas. We also prove that the compactness of the gas contained inside a sphere centered at the origin satisfies the well-known Buchdahl bound, independent of the radius of the sphere. Further, we derive the equation of state for an ideal, classical monoatomic relativistic gas from statistical mechanics considerations and show that it satisfies our assumptions for the existence of a unique solution describing a finite radius star. Although none of the results discussed in this article are new, they are usually scattered in different articles and books in the literature; hence it is our hope that this article will provide a self-contained and useful introduction to the topic of relativistic stellar models.
