多面体的稳定性
Stability of Polytropes
摘要：
本文研究了一些理想星的稳定性。它的目的是作为广义相对论的研究，重点是与物质的耦合，最终旨在更好地理解非常强的引力场和黑洞。这项工作是基于一个完整的度量和物质场系统的作用原理。我们建议对边界条件的处理作一个完全的修正。在我们的术语中，理想恒星具有球对称性和等熵状态方程。在我们关于这个问题的第一项工作中，我们假设密度在离原点有限距离之外为零。但是很难决定适当的边界条件应该是什么，因此我们对固定边界的概念持怀疑态度。在本文中，我们调查的双重多变，其特征在于多变指数n小于5的大部分的恒星和一个大于5的值在外层大气中，延伸到无穷大。它没有固定的边界，但有一个临界密度区域，在这个区域中多变指数从适合恒星体积的值变化到提供大气粗略模型的值。证实了质量和半径之间的关系的存在，以及质量的上限。主要结论是所有的静态位形都是稳定的。
英文摘要：
This paper is an investigation of the stability of some ideal stars. It is in- tended as a study in General Relativity, with emphasis on the coupling to matter, eventually aimed at a better understanding of very strong gravitational fields and Black Holes. The work is based on an action principle for the complete system of metric and matter fields. We propose a complete revision of the treatment of boundary conditions. An ideal star in our terminology has spherical symmetry and an isentropic equation of state. In our first work on this subject it was assumed that the density vanishes beyond a finite distance from the origin. But it is difficult to decide what the proper boundary conditions should be and we are consequently skeptical of the concept of a fixed boundary. In this paper we investigate the double polytrope, characterized by a polytropic index n less than 5 in the bulk of the star and a value larger than 5 in an outer atmosphere that extends to infinity. It has no fixed boundary but a region of critical density where the polytropic index changes from a value that is appropriate for the bulk of the star to a value that provides a crude model for the atmosphere. The existence of a relation between mass and radius is confirmed, as well as an upper limit on the mass. The principal conclusion is that all the static configurations are stable.
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。
