Brill-Lindquist-Riemann和及其极限
Brill-Lindquist-Riemann sums and their limits
摘要：
本文从相对论初始数据的角度出发，研究了离散点-物体组态（我们称之为Brill-Lindquist-Riemann和）向带电尘埃连续统的收敛性。我们的动机是解释的布里-林奎斯特-黎曼和相对孤立的天体，如宇宙中的恒星和星系的集合，和解释的尘埃连续作为宇宙本身。我们的工作开始于建立Brill-Lindquist度量的视界/极小曲面在点源（“星”）附近的存在性和唯一性。然后研究了这些极小曲面外区域的几何性质，讨论了它们的Gromov-Hausdorff极限和内禀平坦极限。一个有趣的和纯粹的几何副产品，我们的工作是例子中，数量曲率跳跃采取Gromov-Hausdorff和/或内在平坦的限制。
英文摘要：
This article commences a study of convergence of discretized point-object configurations, which we call Brill-Lindquist-Riemann sums, towards a charged dust continuum from the perspective of relativistic initial data. We are motivated by the interpretation of Brill-Lindquist-Riemann sums as collections of relatively isolated astrophysical bodies such as stars and galaxies in the universe, and the interpretation of the dust continuum as the universe itself. Our work begins by establishing the existence and the uniqueness of horizons/minimal surfaces of Brill-Lindquist metrics in the vicinity of the point-sources ("stars"). We then study the geometries of the regions exterior to said minimal surfaces, and discuss their Gromov-Hausdorff and intrinsic flat limit. An interesting and purely geometric byproduct of our work are examples in which the scalar curvature jumps upon taking Gromov-Hausdorff and /or intrinsic flat limits.
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。
